Edit Profile (opens in new tab) Kanovei, Vladimir G. Co-Author Distance Author ID: kanovei.vladimir-g Published as: Kanovei, Vladimir; Kanovej, V. G.; Kanovei, V. G.; Kanovei, V.; Kanovei, Vladimir G.; Kanoveĭ, V. G.; Kanoveǐ, V. G.; Kanovej, V. more...less External Links: ORCID · Wikidata · Math-Net.Ru · GND · IdRef Documents Indexed: 191 Publications since 1973, including 4 Books and 27 Additional arXiv Preprints 3 Contributions as Editor Co-Authors: 55 Co-Authors with 121 Joint Publications 1,190 Co-Co-Authors all top 5 Co-Authors 73 single-authored 48 Lyubetsky, Vassily Aleksandrovich 27 Reeken, Michael 25 Katz, Mikhail G. 13 Błaszczyk, Piotr 13 Sherry, David M. 12 Katz, Karin Usadi 8 Kutateladze, Semën Samsonovich 7 Bair, Jacques 7 Uspenskiĭ, Vladimir Andreevich 5 McGaffey, Thomas 5 Mormann, Thomas 5 Nowik, Tahl 5 Schaps, David M. 3 Bascelli, Tiziana 3 Borovik, Alexandre V. 3 Ely, Robert 3 Felgner, Ulrich 3 Hausdorff, Felix 3 Heinig, Peter 3 Henry, Valérie 3 Koepke, Peter 3 Kudryk, Taras S. 3 Purkert, Walter 3 Shnider, Steven 2 Bottazzi, Emanuele 2 Enayat, Ali 2 Friedman, Sy-David 2 Grishin, V. N. 2 Herrlich, Horst 2 Herzberg, Frederik S. 2 Hušek, Miroslav 2 Preuß, Gerhard 2 Sanders, Sam 2 Scholz, Erhard 2 Zapletal, Jindřich 1 Bagaria, Joan 1 Brieskorn, Egbert 1 Chatterji, Srishti Dhar 1 Christensen, Jens Peter Reus 1 Durand, Bruno 1 Epple, Moritz 1 Fëdorov, Vladimir Semënovich 1 Fletcher, Peter 1 Gitman, Victoria 1 Golshani, Mohammad 1 Guillén, Elías Fuentes 1 Hrbáček, Karel 1 Lobry, Claude 1 Ostrovsky, Alexey Vladimirovich 1 Reeder, Patrick 1 Sabok, Marcin 1 Schaps, Mary Elizabeth 1 Schindler, Ralf-Dieter 1 Shelah, Saharon 1 Ugaglia, Monica 1 van Lambalgen, Michiel Marian Michiel 1 Vereshchagin, Nikolay K. all top 5 Serials 21 Mathematical Notes 9 Mathematical Logic Quarterly (MLQ) 7 Russian Mathematical Surveys 7 The Journal of Symbolic Logic 7 Foundations of Science 6 Fundamenta Mathematicae 6 Siberian Mathematical Journal 6 Soviet Mathematics. Doklady 6 Annals of Pure and Applied Logic 5 Real Analysis Exchange 5 Studia Logica 4 Matematicheskie Zametki 4 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 4 Archive for Mathematical Logic 4 Izvestiya: Mathematics 3 Moscow University Mathematics Bulletin 3 Topology and its Applications 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 Applied Mathematics and Computation 2 Mathematica Japonica 2 Mathematics of the USSR. Izvestiya 2 Monatshefte für Mathematik 2 Proceedings of the American Mathematical Society 2 Sibirskiĭ Matematicheskiĭ Zhurnal 2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 2 Notices of the American Mathematical Society 2 Matematychni Studiï 2 Journal of Mathematical Logic 2 Proceedings of the Steklov Institute of Mathematics 2 Antiquitates Mathematicae 2 Open Mathematics 1 The Mathematical Intelligencer 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Journal of Soviet Mathematics 1 Mathematika 1 Notre Dame Journal of Formal Logic 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 Mathematics of the USSR, Sbornik 1 Journal of Mathematical Sciences (New York) 1 Itogi Nauki i Tekhniki. Seriya Algebra. Topologiya. Geometriya 1 Sbornik: Mathematics 1 Cambridge Tracts in Mathematics 1 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 1 University Lecture Series 1 Logica Universalis 1 Journal of Humanistic Mathematics 1 Quantum Studies: Mathematics and Foundations 1 Springer Monographs in Mathematics 1 British Journal for the History of Mathematics all top 5 Fields 168 Mathematical logic and foundations (03-XX) 24 History and biography (01-XX) 20 Real functions (26-XX) 12 Measure and integration (28-XX) 8 General topology (54-XX) 4 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Group theory and generalizations (20-XX) 2 Sequences, series, summability (40-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 111 Publications have been cited 608 times in 271 Documents Cited by ▼ Year ▼ Borel equivalence relations. Structure and classification. Zbl 1155.03035 Kanovei, Vladimir G. 58 2008 Nonstandard analysis, axiomatically. Zbl 1058.03002 Kanovei, V.; Reeken, Michael 43 2004 Canonical Ramsey theory on Polish spaces. Zbl 1278.03001 Kanovei, Vladimir; Sabok, Marcin; Zapletal, Jindřich 27 2013 Fermat, Leibniz, Euler, and the gang: the true history of the concepts of limit and shadow. Zbl 1338.26001 Bascelli, Tiziana; Bottazzi, Emanuele; Herzberg, Frederik; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Nowik, Tahl; Sherry, David; Shnider, Steven 21 2014 A countable definable set containing no definable elements. Zbl 1420.03130 Kanovei, V. G.; Lyubetsky, V. A. 18 2017 Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Zbl 1435.03094 Fletcher, Peter; Hrbacek, Karel; Kanovei, Vladimir; Katz, Mikhail G.; Lobry, Claude; Sanders, Sam 18 2017 Is mathematical history written by the victors? Zbl 1334.01010 Bair, Jacques; Błaszczyk, Piotr; Ely, Robert; Henry, Valérie; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David; Shnider, Steven 18 2013 A definable nonstandard model of the reals. Zbl 1070.03044 Kanovei, Vladimir; Shelah, Saharon 16 2004 A definable \(E_0\) class containing no definable elements. Zbl 1343.03040 Kanovei, Vladimir; Lyubetsky, Vassily 13 2015 Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics. Zbl 1392.03012 Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas 13 2013 On non-wellfounded iterations of the perfect set forcing. Zbl 0930.03062 Kanovei, Vladimir 12 1999 A model of second-order arithmetic satisfying AC but not DC. Zbl 1484.03067 Friedman, Sy-David; Gitman, Victoria; Kanovei, Vladimir 10 2019 On some classical problems in descriptive set theory. Zbl 1064.03031 Kanovej, V. G.; Lyubetskij, V. A. 10 2003 A Groszek-Laver pair of undistinguishable \(\mathsf{E}_0\)-classes. Zbl 1437.03146 Golshani, Mohammad; Kanovei, Vladimir; Lyubetsky, Vassily 10 2017 An Ulm-type classification theorem for equivalence relations in Solovay model. Zbl 0895.03020 Kanovei, Vladimir 10 1997 Counterexamples to countable-section \(\varPi_2^1\) uniformization and \(\varPi_3^1\) separation. Zbl 1403.03086 Kanovei, Vladimir; Lyubetsky, Vassily 9 2016 Internal approach to external sets and universes. I: Bounded set theory. Zbl 0837.03048 Kanovei, Vladimir; Reeken, Michael 9 1995 Toward a history of mathematics focused on procedures. Zbl 1398.01005 Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; Sherry, David 9 2017 Undecidable hypotheses in Edward Nelson’s internal set theory. Zbl 0782.03028 Kanovej, V. G. 8 1991 Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes. Zbl 1446.03081 Kanovei, Vladimir G.; Lyubetsky, Vassily A. 7 2018 Cauchy, infinitesimals and ghosts of departed quantifiers. Zbl 1476.01006 Bair, J.; Błaszczyk, P.; Ely, R.; Henry, V.; Kanovei, V.; Katz, K. U.; Katz, M. G.; Kudryk, T.; Kutateladze, S. S.; McGaffey, T.; Mormann, T.; Schaps, D. M.; Sherry, D. 7 2017 Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy. Zbl 1472.03059 Kanovei, Vladimir; Lyubetsky, Vassily 7 2019 Countable OD sets of reals belong to the ground model. Zbl 1522.03195 Kanovei, Vladimir; Lyubetsky, Vassily 7 2018 Controversies in the foundations of analysis: comments on Schubring’s Conflicts. Zbl 1368.01021 Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Mikhail G.; Sherry, David 6 2017 Euler’s lute and Edwards’s oud. Zbl 1342.01017 Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Sherry, David 6 2015 Definable \(\mathsf{E}_0\) classes at arbitrary projective levels. Zbl 1426.03028 Kanovei, Vladimir; Lyubetsky, Vassily 6 2018 Non-Glimm-Effros equivalence relations at second projective level. Zbl 0883.03034 Kanovei, Vladimir 6 1997 When a partial Borel order is linearizable. Zbl 0909.03041 Kanovei, Vladimir 6 1998 Problems of set-theoretic non-standard analysis. Zbl 1226.03067 Kanoveĭ, V. G.; Lyubetskiĭ, V. A. 5 2007 Proofs and retributions, or: why Sarah can’t take limits. Zbl 1368.00021 Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Schaps, Mary 5 2015 Uniqueness, collection, and external collapse of cardinals in IST and models of Peano arithmetic. Zbl 0820.03034 Kanovei, V. 5 1995 Internal approach to external sets and universes. II: External universes over the universe of bounded set theory. Zbl 0855.03042 Kanovei, Vladimir; Reeken, Michael 5 1995 An effective minimal encoding of uncountable sets. Zbl 1252.03113 Kanovei, V. G.; Lyubetsky, V. A. 5 2011 Continuity between Cauchy and Bolzano: issues of antecedents and priority. Zbl 1461.01010 Bair, Jacques; Błaszczyk, Piotr; Fuentes Guillén, Elías; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G. 5 2020 Gregory’s sixth operation. Zbl 1398.01052 Bascelli, Tiziana; Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; Nowik, Tahl; Schaps, David M.; Sherry, David 5 2018 New Radon-Nikodym ideals. Zbl 1025.03045 Kanovei, Vladimir; Reeken, Michael 5 2000 Collected works. Vol. III: Set theory (1927, 1935). Descriptive set theory and topology. Edited by U. Felgner, H. Herrlich, M. Hušek, V. Kanovei, P. Koepke, G. Preuß, W. Purkert und E. Scholz. (Gesammelte Werke. Band III: Mengenlehre (1927, 1935). Deskriptive Mengenlehre und Topologie.) Zbl 1149.01022 Hausdorff, Felix 4 2008 Generalization of one construction by Solovay. Zbl 1347.03090 Kanovei, V. G.; Lyubetsky, V. A. 4 2015 Small oscillations of the pendulum, Euler’s method, and adequality. Zbl 1404.70014 Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Nowik, Tahl 4 2016 Internal approach to external sets and universes. III. Partially saturated universes. Zbl 0855.03043 Kanovei, Vladimir; Reeken, Michael 4 1996 On the nonemptiness of classes in axiomatic set theory. Zbl 0427.03044 Kanovej, V. G. 4 1978 An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited. Zbl 1547.03313 Enayat, Ali; Kanovei, Vladimir 4 2021 Definable minimal collapse functions at arbitrary projective levels. Zbl 1453.03053 Kanovei, Vladimir; Lyubetsky, Vassily 4 2019 A generic property of the Solovay set \(\Sigma\). Zbl 1420.03133 Kanovei, V. G.; Lyubetsky, V. A. 4 2017 Minimal axiomatic frameworks for definable hyperreals with transfer. Zbl 1447.03014 Herzberg, Frederik S.; Kanovei, Vladimir; Katz, Mikhail; Lyubetsky, Vassily 4 2018 Cauchy’s infinitesimals, his sum theorem, and foundational paradigms. Zbl 1398.01014 Bascelli, Tiziana; Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David 4 2018 Mathematics in a nonstandard world. I. Zbl 0887.03044 Kanovei, Vladimir; Reeken, Michael 4 1997 Two dichotomy theorems on colourability of non-analytic graphs. Zbl 0883.03035 Kanovei, Vladimir 4 1997 Kolmogorov’s ideas in the theory of operations on sets. Zbl 0671.04001 Kanovej, V. G. 4 1988 On Ulam’s problem of stability of non-exact homomorphisms. Zbl 0995.03036 Kanovej, V.; Reeken, M. 4 2000 Some new results on the Borel irreducibility of equivalence relations. Zbl 1068.03036 Kanovej, V. G.; Reeken, M. 4 2003 On mathematical realism and applicability of hyperreals. Zbl 1436.00032 Bottazzi, E.; Kanovei, V.; Katz, M.; Mormann, T.; Sherry, D. 4 2019 A non-standard analysis of a cultural icon: the case of Paul Halmos. Zbl 1365.01032 Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Mikhail G.; Kudryk, Taras; Kutateladze, Semen S.; Sherry, David 4 2016 On Baire measurable homomorphisms of quotients of the additive group of the reals. Zbl 0972.03045 Kanovei, Vladimir; Reeken, Michael 4 2000 What makes a theory of infinitesimals useful? A view by Klein and Fraenkel. Zbl 1522.03352 Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Mormann, Thomas 4 2018 Borel OD sets of reals are OD-Borel in some simple models. Zbl 1537.03061 Kanovei, Vladimir; Lyubetsky, Vassily 3 2019 On coding uncountable sets by reals. Zbl 1200.03032 Bagaria, Joan; Kanovei, Vladimir 3 2010 Linearization of definable order relations. Zbl 0942.03055 Kanovei, Vladimir 3 2000 On discriptive forms of the countable axiom of choice. Zbl 0439.03033 Kanovej, V. G. 3 1979 The set of all analytically definable sets of natural numbers can be defined analytically. Zbl 0452.03041 Kanovej, V. G. 3 1980 A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory. Zbl 1423.03180 Kanovei, Vladimir; Katz, Mikhail 3 2017 Models of set theory in which the separation theorem fails. Zbl 07480690 Kanovei, Vladimir G.; Lyubetsky, Vassily A. 3 2021 Collected works. Vol. II: Foundations of set theory. (Gesammelte Werke. Band II: Grundzüge der Mengenlehre. Herausgegeben von E. Brieskorn, S. D. Chatterji, M. Epple, U. Felgner, H. Herrlich, M. Hušek, V. Kanovei, P. Koepke, G. Preuß, W. Purkert und E. Scholz.) Zbl 1010.01031 Hausdorff, Felix 3 2002 Cauchy’s work on integral geometry, centers of curvature, and other applications of infinitesimals. Zbl 1442.01010 Bair, Jacques; Błaszczyk, Piotr; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G.; McGaffey, Thomas 3 2020 Topologies generated by effectively Suslin sets, and their applications in descriptive set theory. Zbl 0878.54022 Kanovei, V. G. 3 1996 A theorem on ROD-hypersmooth equivalence relations in the Solovay model. Zbl 1026.03033 Kanovei, Vladimir; Reeken, Michael 3 2003 19th-century real analysis, forward and backward. Zbl 1523.01006 Bair, Jacques; Błaszczyk, Piotr; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G. 3 2019 Some natural equivalence relations in the Solovay model. Zbl 1204.03048 Friedman, Sy-David; Kanovei, Vladimir 2 2008 On Hausdorff ordered structures. Zbl 1220.03045 Kanoveĭ, V. G. 2 2009 Lebesgue measure and gambling. Zbl 1171.28300 Kanoveǐ, V. G.; Linton, T.; Uspensky, V. A. 2 2008 Grossone approach to Hutton and Euler transforms. Zbl 1338.68300 Kanovei, Vladimir; Lyubetsky, Vassily 2 2015 Cardinality of the set of Vitali equivalence classes. Zbl 0742.03016 Kanovej, V. G. 2 1991 Ulm classification of analytic equivalence relations in generic universes. Zbl 0921.03048 Kanovei, Vladimir 2 1998 Uniqueness of nonstandard extensions. Zbl 1150.03311 Kanovej, V. G.; Uspenskij, V. A. 2 2006 Über das Nichtleersein von Klassen in der axiomatischen Mengentheorie. Zbl 0409.03031 Kanovei, V. G. 2 1978 The full basis theorem does not imply analytic wellordering. Zbl 1528.03199 Kanovei, Vladimir; Lyubetsky, Vassily 2 2021 On the equality relation modulo a countable set. Zbl 1485.03199 Kanovei, V. G.; Lyubetsky, V. A. 2 2020 On effective \(\sigma \)-boundedness and \(\sigma \)-compactness. Zbl 1283.03080 Kanovei, Vladimir; Lyubetsky, Vassily 2 2013 On Ulam stability of the real line. Zbl 0994.03040 Kanovei, Vladimir; Reeken, Michael 2 2001 A cofinal family of equivalence relations and Borel ideals generating them. Zbl 1351.37015 Kanovei, V. G.; Lyubetsky, V. A. 2 2006 The correctness of Euler’s method for the factorization of the sine function into an infinite product. Zbl 0713.41013 Kanovej, V. G. 2 1988 The axiom of choice and the axiom of determinateness. (Aksioma vybora i aksioma determinirovannosti). Zbl 0599.03053 Kanovej, V. G. 2 1984 A nonstandard set theory in the \(\in\)-language. Zbl 1002.03044 Kanovei, Vladimir; Reeken, Michael 2 2000 Extending standard models of ZFC to models of nonstandard set theories. Zbl 0969.03072 Kanovei, Vladimir; Reeken, Michael 2 2000 An infinity which depends on the axiom of choice. Zbl 1254.03086 Kanovei, Vladimir; Lyubetsky, Vassily 2 2012 On the cardinality of the set of Vitali equivalence classes. Zbl 0729.03027 Kanovej, V. G. 1 1991 On countable cofinality and decomposition of definable thin orderings. Zbl 1432.03089 Kanovei, Vladimir; Lyubetsky, Vassily 1 2016 Definable Hamel bases and \(\mathsf{AC}_{\omega} (\mathbb{R})\). Zbl 1485.03200 Kanovei, Vladimir; Schindler, Ralf 1 2021 On external Scott algebras in nonstandard models of Peano arithmetic. Zbl 0859.03034 Kanovei, Vladimir 1 1996 On initial segments of degrees of constructibility. Zbl 0344.02046 Kanovei, V. G. 1 1975 The set of all analytically definable sets of natural numbers may be analytically definable. Zbl 0427.03045 Kanovej, V. G. 1 1979 Is Leibnizian calculus embeddable in first order logic? Zbl 1398.03223 Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kudryk, Taras; Mormann, Thomas; Sherry, David 1 2017 Mathematics in a nonstandard world. II. Zbl 0894.03037 Kanovei, Vladimir; Reeken, Michael 1 1997 On “star” schemata of Kossak and Paris. Zbl 0917.03019 Kanovei, Vladimir 1 1998 The axiom of determinacy and the modern development of descriptive set theory. Zbl 0636.03046 Kanovej, V. G. 1 1988 Borel and countably determined reducibility in nonstandard domain. Zbl 1084.03051 Kanovei, Vladimir; Reeken, Michael 1 2003 The development of the descriptive theory of sets under the influence of the work of Luzin. Zbl 0595.01009 Kanovej, V. G. 1 1985 Undecidable and decidable properties of constituents. Zbl 0598.03041 Kanovej, V. G. 1 1985 Historical infinitesimalists and modern historiography of infinitesimals. Zbl 07866951 Bair, Jacques; Katz, Mikhail; Borovik, Alexandre; Kanovei, Vladimir; Kutateladze, Semen S.; Sanders, Sam; Sherry, David; Ugaglia, Monica 1 2022 Isomorphism property in nonstandard extensions of the \(\mathbf Z\mathbf F\mathbf C\) universe. Zbl 0883.03040 Kanovei, Vladimir; Reeken, Michael 1 1997 Historical infinitesimalists and modern historiography of infinitesimals. Zbl 07866951 Bair, Jacques; Katz, Mikhail; Borovik, Alexandre; Kanovei, Vladimir; Kutateladze, Semen S.; Sanders, Sam; Sherry, David; Ugaglia, Monica 1 2022 On the ‘definability of definable’ problem of Alfred Tarski. II. Zbl 07612776 Kanovei, Vladimir; Lyubetsky, Vassily 1 2022 An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited. Zbl 1547.03313 Enayat, Ali; Kanovei, Vladimir 4 2021 Models of set theory in which the separation theorem fails. Zbl 07480690 Kanovei, Vladimir G.; Lyubetsky, Vassily A. 3 2021 The full basis theorem does not imply analytic wellordering. Zbl 1528.03199 Kanovei, Vladimir; Lyubetsky, Vassily 2 2021 Definable Hamel bases and \(\mathsf{AC}_{\omega} (\mathbb{R})\). Zbl 1485.03200 Kanovei, Vladimir; Schindler, Ralf 1 2021 Continuity between Cauchy and Bolzano: issues of antecedents and priority. Zbl 1461.01010 Bair, Jacques; Błaszczyk, Piotr; Fuentes Guillén, Elías; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G. 5 2020 Cauchy’s work on integral geometry, centers of curvature, and other applications of infinitesimals. Zbl 1442.01010 Bair, Jacques; Błaszczyk, Piotr; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G.; McGaffey, Thomas 3 2020 On the equality relation modulo a countable set. Zbl 1485.03199 Kanovei, V. G.; Lyubetsky, V. A. 2 2020 A model of second-order arithmetic satisfying AC but not DC. Zbl 1484.03067 Friedman, Sy-David; Gitman, Victoria; Kanovei, Vladimir 10 2019 Non-uniformizable sets with countable cross-sections on a given level of the projective hierarchy. Zbl 1472.03059 Kanovei, Vladimir; Lyubetsky, Vassily 7 2019 Definable minimal collapse functions at arbitrary projective levels. Zbl 1453.03053 Kanovei, Vladimir; Lyubetsky, Vassily 4 2019 On mathematical realism and applicability of hyperreals. Zbl 1436.00032 Bottazzi, E.; Kanovei, V.; Katz, M.; Mormann, T.; Sherry, D. 4 2019 Borel OD sets of reals are OD-Borel in some simple models. Zbl 1537.03061 Kanovei, Vladimir; Lyubetsky, Vassily 3 2019 19th-century real analysis, forward and backward. Zbl 1523.01006 Bair, Jacques; Błaszczyk, Piotr; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G. 3 2019 Definable elements of definable Borel sets. Zbl 1529.03250 Kanovei, V. G.; Lyubetsky, V. A. 1 2019 Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes. Zbl 1446.03081 Kanovei, Vladimir G.; Lyubetsky, Vassily A. 7 2018 Countable OD sets of reals belong to the ground model. Zbl 1522.03195 Kanovei, Vladimir; Lyubetsky, Vassily 7 2018 Definable \(\mathsf{E}_0\) classes at arbitrary projective levels. Zbl 1426.03028 Kanovei, Vladimir; Lyubetsky, Vassily 6 2018 Gregory’s sixth operation. Zbl 1398.01052 Bascelli, Tiziana; Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; Nowik, Tahl; Schaps, David M.; Sherry, David 5 2018 Minimal axiomatic frameworks for definable hyperreals with transfer. Zbl 1447.03014 Herzberg, Frederik S.; Kanovei, Vladimir; Katz, Mikhail; Lyubetsky, Vassily 4 2018 Cauchy’s infinitesimals, his sum theorem, and foundational paradigms. Zbl 1398.01014 Bascelli, Tiziana; Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David 4 2018 What makes a theory of infinitesimals useful? A view by Klein and Fraenkel. Zbl 1522.03352 Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Mormann, Thomas 4 2018 A countable definable set containing no definable elements. Zbl 1420.03130 Kanovei, V. G.; Lyubetsky, V. A. 18 2017 Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Zbl 1435.03094 Fletcher, Peter; Hrbacek, Karel; Kanovei, Vladimir; Katz, Mikhail G.; Lobry, Claude; Sanders, Sam 18 2017 A Groszek-Laver pair of undistinguishable \(\mathsf{E}_0\)-classes. Zbl 1437.03146 Golshani, Mohammad; Kanovei, Vladimir; Lyubetsky, Vassily 10 2017 Toward a history of mathematics focused on procedures. Zbl 1398.01005 Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; Sherry, David 9 2017 Cauchy, infinitesimals and ghosts of departed quantifiers. Zbl 1476.01006 Bair, J.; Błaszczyk, P.; Ely, R.; Henry, V.; Kanovei, V.; Katz, K. U.; Katz, M. G.; Kudryk, T.; Kutateladze, S. S.; McGaffey, T.; Mormann, T.; Schaps, D. M.; Sherry, D. 7 2017 Controversies in the foundations of analysis: comments on Schubring’s Conflicts. Zbl 1368.01021 Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Mikhail G.; Sherry, David 6 2017 A generic property of the Solovay set \(\Sigma\). Zbl 1420.03133 Kanovei, V. G.; Lyubetsky, V. A. 4 2017 A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory. Zbl 1423.03180 Kanovei, Vladimir; Katz, Mikhail 3 2017 Is Leibnizian calculus embeddable in first order logic? Zbl 1398.03223 Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kudryk, Taras; Mormann, Thomas; Sherry, David 1 2017 Counterexamples to countable-section \(\varPi_2^1\) uniformization and \(\varPi_3^1\) separation. Zbl 1403.03086 Kanovei, Vladimir; Lyubetsky, Vassily 9 2016 Small oscillations of the pendulum, Euler’s method, and adequality. Zbl 1404.70014 Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Nowik, Tahl 4 2016 A non-standard analysis of a cultural icon: the case of Paul Halmos. Zbl 1365.01032 Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Mikhail G.; Kudryk, Taras; Kutateladze, Semen S.; Sherry, David 4 2016 On countable cofinality and decomposition of definable thin orderings. Zbl 1432.03089 Kanovei, Vladimir; Lyubetsky, Vassily 1 2016 A definable \(E_0\) class containing no definable elements. Zbl 1343.03040 Kanovei, Vladimir; Lyubetsky, Vassily 13 2015 Euler’s lute and Edwards’s oud. Zbl 1342.01017 Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Sherry, David 6 2015 Proofs and retributions, or: why Sarah can’t take limits. Zbl 1368.00021 Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Schaps, Mary 5 2015 Generalization of one construction by Solovay. Zbl 1347.03090 Kanovei, V. G.; Lyubetsky, V. A. 4 2015 Grossone approach to Hutton and Euler transforms. Zbl 1338.68300 Kanovei, Vladimir; Lyubetsky, Vassily 2 2015 Fermat, Leibniz, Euler, and the gang: the true history of the concepts of limit and shadow. Zbl 1338.26001 Bascelli, Tiziana; Bottazzi, Emanuele; Herzberg, Frederik; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Nowik, Tahl; Sherry, David; Shnider, Steven 21 2014 Canonical Ramsey theory on Polish spaces. Zbl 1278.03001 Kanovei, Vladimir; Sabok, Marcin; Zapletal, Jindřich 27 2013 Is mathematical history written by the victors? Zbl 1334.01010 Bair, Jacques; Błaszczyk, Piotr; Ely, Robert; Henry, Valérie; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David; Shnider, Steven 18 2013 Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics. Zbl 1392.03012 Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas 13 2013 On effective \(\sigma \)-boundedness and \(\sigma \)-compactness. Zbl 1283.03080 Kanovei, Vladimir; Lyubetsky, Vassily 2 2013 Felix Hausdorff. Collected works. Volume IA. General set theory. Edited by Ulrich Felgner, Vladimir Kanovei, Peter Koepke and Walter Purkert. (Gesammelte Werke. Band IA. Allgemeine Mengenlehre.) Zbl 1515.01034 Hausdorff, Felix 1 2013 An infinity which depends on the axiom of choice. Zbl 1254.03086 Kanovei, Vladimir; Lyubetsky, Vassily 2 2012 Effective compactness and sigma-compactness. Zbl 1286.03144 Kanovei, V. G.; Lyubetsky, V. A. 1 2012 An effective minimal encoding of uncountable sets. Zbl 1252.03113 Kanovei, V. G.; Lyubetsky, V. A. 5 2011 On coding uncountable sets by reals. Zbl 1200.03032 Bagaria, Joan; Kanovei, Vladimir 3 2010 On Hausdorff ordered structures. Zbl 1220.03045 Kanoveĭ, V. G. 2 2009 Borel equivalence relations. Structure and classification. Zbl 1155.03035 Kanovei, Vladimir G. 58 2008 Collected works. Vol. III: Set theory (1927, 1935). Descriptive set theory and topology. Edited by U. Felgner, H. Herrlich, M. Hušek, V. Kanovei, P. Koepke, G. Preuß, W. Purkert und E. Scholz. (Gesammelte Werke. Band III: Mengenlehre (1927, 1935). Deskriptive Mengenlehre und Topologie.) Zbl 1149.01022 Hausdorff, Felix 4 2008 Some natural equivalence relations in the Solovay model. Zbl 1204.03048 Friedman, Sy-David; Kanovei, Vladimir 2 2008 Lebesgue measure and gambling. Zbl 1171.28300 Kanoveǐ, V. G.; Linton, T.; Uspensky, V. A. 2 2008 Problems of set-theoretic non-standard analysis. Zbl 1226.03067 Kanoveĭ, V. G.; Lyubetskiĭ, V. A. 5 2007 Uniqueness of nonstandard extensions. Zbl 1150.03311 Kanovej, V. G.; Uspenskij, V. A. 2 2006 A cofinal family of equivalence relations and Borel ideals generating them. Zbl 1351.37015 Kanovei, V. G.; Lyubetsky, V. A. 2 2006 Nonstandard analysis, axiomatically. Zbl 1058.03002 Kanovei, V.; Reeken, Michael 43 2004 A definable nonstandard model of the reals. Zbl 1070.03044 Kanovei, Vladimir; Shelah, Saharon 16 2004 On some classical problems in descriptive set theory. Zbl 1064.03031 Kanovej, V. G.; Lyubetskij, V. A. 10 2003 Some new results on the Borel irreducibility of equivalence relations. Zbl 1068.03036 Kanovej, V. G.; Reeken, M. 4 2003 A theorem on ROD-hypersmooth equivalence relations in the Solovay model. Zbl 1026.03033 Kanovei, Vladimir; Reeken, Michael 3 2003 Borel and countably determined reducibility in nonstandard domain. Zbl 1084.03051 Kanovei, Vladimir; Reeken, Michael 1 2003 Do stronger definitions of randomness exist? Zbl 1044.68073 Durand, Bruno; Kanovei, Vladimir; Uspensky, Vladimir A.; Vereshchagin, Nikolai 1 2003 Collected works. Vol. II: Foundations of set theory. (Gesammelte Werke. Band II: Grundzüge der Mengenlehre. Herausgegeben von E. Brieskorn, S. D. Chatterji, M. Epple, U. Felgner, H. Herrlich, M. Hušek, V. Kanovei, P. Koepke, G. Preuß, W. Purkert und E. Scholz.) Zbl 1010.01031 Hausdorff, Felix 3 2002 On Ulam stability of the real line. Zbl 0994.03040 Kanovei, Vladimir; Reeken, Michael 2 2001 On Borel orderable groups. Zbl 0968.03054 Christensen, J. P. R.; Kanovei, Vladimir; Reeken, Michael 1 2001 New Radon-Nikodym ideals. Zbl 1025.03045 Kanovei, Vladimir; Reeken, Michael 5 2000 On Ulam’s problem of stability of non-exact homomorphisms. Zbl 0995.03036 Kanovej, V.; Reeken, M. 4 2000 On Baire measurable homomorphisms of quotients of the additive group of the reals. Zbl 0972.03045 Kanovei, Vladimir; Reeken, Michael 4 2000 Linearization of definable order relations. Zbl 0942.03055 Kanovei, Vladimir 3 2000 A nonstandard set theory in the \(\in\)-language. Zbl 1002.03044 Kanovei, Vladimir; Reeken, Michael 2 2000 Extending standard models of ZFC to models of nonstandard set theories. Zbl 0969.03072 Kanovei, Vladimir; Reeken, Michael 2 2000 On non-wellfounded iterations of the perfect set forcing. Zbl 0930.03062 Kanovei, Vladimir 12 1999 Extension of standard models of ZFC to models of Nelson’s nonstandard set theory IST. Zbl 0955.03070 Kanovei, V. G.; Reeken, M. 1 1999 A nonstandard proof of the Jordan curve theorem. Zbl 0938.54041 Kanovei, Vladimir; Reeken, Michael 1 1999 When a partial Borel order is linearizable. Zbl 0909.03041 Kanovei, Vladimir 6 1998 Ulm classification of analytic equivalence relations in generic universes. Zbl 0921.03048 Kanovei, Vladimir 2 1998 On “star” schemata of Kossak and Paris. Zbl 0917.03019 Kanovei, Vladimir 1 1998 Elementary extensions of external classes in a nonstandard universe. Zbl 0956.03054 Kanovei, Vladimir; Reeken, Michael 1 1998 An Ulm-type classification theorem for equivalence relations in Solovay model. Zbl 0895.03020 Kanovei, Vladimir 10 1997 Non-Glimm-Effros equivalence relations at second projective level. Zbl 0883.03034 Kanovei, Vladimir 6 1997 Mathematics in a nonstandard world. I. Zbl 0887.03044 Kanovei, Vladimir; Reeken, Michael 4 1997 Two dichotomy theorems on colourability of non-analytic graphs. Zbl 0883.03035 Kanovei, Vladimir 4 1997 Mathematics in a nonstandard world. II. Zbl 0894.03037 Kanovei, Vladimir; Reeken, Michael 1 1997 Isomorphism property in nonstandard extensions of the \(\mathbf Z\mathbf F\mathbf C\) universe. Zbl 0883.03040 Kanovei, Vladimir; Reeken, Michael 1 1997 Internal approach to external sets and universes. III. Partially saturated universes. Zbl 0855.03043 Kanovei, Vladimir; Reeken, Michael 4 1996 Topologies generated by effectively Suslin sets, and their applications in descriptive set theory. Zbl 0878.54022 Kanovei, V. G. 3 1996 On external Scott algebras in nonstandard models of Peano arithmetic. Zbl 0859.03034 Kanovei, Vladimir 1 1996 Internal approach to external sets and universes. I: Bounded set theory. Zbl 0837.03048 Kanovei, Vladimir; Reeken, Michael 9 1995 Uniqueness, collection, and external collapse of cardinals in IST and models of Peano arithmetic. Zbl 0820.03034 Kanovei, V. 5 1995 Internal approach to external sets and universes. II: External universes over the universe of bounded set theory. Zbl 0855.03042 Kanovei, Vladimir; Reeken, Michael 5 1995 Undecidable hypotheses in Edward Nelson’s internal set theory. Zbl 0782.03028 Kanovej, V. G. 8 1991 Cardinality of the set of Vitali equivalence classes. Zbl 0742.03016 Kanovej, V. G. 2 1991 On the cardinality of the set of Vitali equivalence classes. Zbl 0729.03027 Kanovej, V. G. 1 1991 Kolmogorov’s ideas in the theory of operations on sets. Zbl 0671.04001 Kanovej, V. G. 4 1988 The correctness of Euler’s method for the factorization of the sine function into an infinite product. Zbl 0713.41013 Kanovej, V. G. 2 1988 The axiom of determinacy and the modern development of descriptive set theory. Zbl 0636.03046 Kanovej, V. G. 1 1988 ...and 11 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 229 Authors 71 Kanovei, Vladimir G. 34 Lyubetsky, Vassily Aleksandrovich 32 Katz, Mikhail G. 13 Sherry, David M. 11 Błaszczyk, Piotr 10 Kutateladze, Semën Samsonovich 10 Reeken, Michael 9 Katz, Karin Usadi 9 Sanders, Sam 8 Van den Berg, Imme Pieter 8 Zapletal, Jindřich 6 Friedman, Sy-David 6 Hrbáček, Karel 5 Bair, Jacques 5 Kuhlemann, Karl 4 Bottazzi, Emanuele 4 Ding, Longyun 4 Dinis, Bruno 4 Heinig, Peter 4 Kudryk, Taras S. 4 Nowik, Tahl 4 Shani, Assaf 4 Shelah, Saharon 4 Thomas, Simon R. 4 Tran, Nam-Van 3 Borovik, Alexandre V. 3 Doucha, Michal 3 Enayat, Ali 3 Gitman, Victoria 3 Larson, Paul B. 3 Miller, Benjamin David 3 Mormann, Thomas 3 Panagiotopoulos, Aristotelis 3 Pruss, Alexander R. 3 Sabok, Marcin 3 Ugaglia, Monica 2 Abdul-Quader, Athar 2 Andreev, P. V. 2 Arthur, Richard T. W. 2 Bascelli, Tiziana 2 Bazhenov, Nikolaĭ Alekseevich 2 Bezuglyi, Sergey I. 2 Budinas, B. L. 2 Calderoni, Filippo 2 Clemens, John Daniel 2 Dean, Walter 2 Du, Guoping 2 Farah, Ilijas 2 Forrest, Jeffrey Yi-Lin 2 Gogacz, Tomasz 2 Gong, Ningsheng 2 Gordon, Evgeniĭ Izrail’evich 2 Herzberg, Frederik S. 2 Imamura, Takuma 2 Impens, Chris 2 Jørgensen, Palle E. T. 2 Kaya, Burak 2 Kusraev, Anatoliĭ Georgievich 2 Matthews, Richard 2 McGaffey, Thomas 2 McKenzie, Zachiri 2 Michalewski, Henryk 2 Mio, Matteo 2 Motto Ros, Luca 2 Müller, Sandra 2 Rabouin, David 2 Schaps, David M. 2 Schlicht, Philipp 2 Schmerl, James H. 2 Schrittesser, David 2 Sergeev, Yaroslav Dmitrievich 2 Skrzypczak, Michał 2 Törnquist, Asger 2 Trlifajová, Kateřina 2 van Atten, Mark 2 Vidnyánszky, Zoltán 2 Williams, Kameryn J. 2 Zakrzewski, Piotr 2 Zhu, Wujia 1 Abdeljalil, Saghe 1 Albeverio, Sergio A. 1 Amodio, Pierluigi 1 Andreev, Petr 1 Andretta, Alessandro 1 Antos, Carolin 1 Bagaria, Joan 1 Baldwin, John T. 1 Barabash, G. M. 1 Bellaouar, Djamel 1 Benci, Vieri 1 Berenguer, Joaquim 1 Bergfalk, Jeffrey 1 Bianchini, Stefano 1 Borodulin-Nadzieja, Piotr 1 Boudaoud, Abdelmadjid 1 Boute, Raymond T. 1 Bowler, Nathan 1 Brendle, Jörg 1 Caravenna, Laura 1 Carmesin, Johannes ...and 129 more Authors all top 5 Cited in 91 Serials 24 The Journal of Symbolic Logic 21 Annals of Pure and Applied Logic 13 Mathematical Logic Quarterly (MLQ) 11 Mathematical Notes 11 Journal of Mathematical Logic 10 Archive for Mathematical Logic 10 Foundations of Science 8 Proceedings of the American Mathematical Society 7 Transactions of the American Mathematical Society 6 Fundamenta Mathematicae 5 Israel Journal of Mathematics 5 Siberian Mathematical Journal 5 Topology and its Applications 5 The Bulletin of Symbolic Logic 4 The Mathematical Intelligencer 4 Notre Dame Journal of Formal Logic 4 Synthese 4 British Journal for the History of Mathematics 3 Studia Logica 3 Indagationes Mathematicae. New Series 3 Erkenntnis 3 The Review of Symbolic Logic 3 Antiquitates Mathematicae 3 Open Mathematics 2 Archive for History of Exact Sciences 2 Journal of Mathematical Analysis and Applications 2 Mathematical Methods in the Applied Sciences 2 Advances in Mathematics 2 Applied Mathematics and Computation 2 Kybernetes 2 Memoirs of the American Mathematical Society 2 Real Analysis Exchange 2 Theoretical Computer Science 2 Optimization 2 Historia Mathematica 2 Journal of Mathematical Sciences (New York) 2 Bulletin des Sciences Mathématiques 2 Izvestiya: Mathematics 2 Matematychni Studiï 2 Logica Universalis 2 Journal of Applied and Industrial Mathematics 2 Journal of Logic and Analysis 2 Special Matrices 1 Russian Mathematical Surveys 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica Vietnamica 1 Canadian Mathematical Bulletin 1 Commentationes Mathematicae Universitatis Carolinae 1 Czechoslovak Mathematical Journal 1 Journal of Combinatorial Theory. Series B 1 Mathematische Annalen 1 Mathematics and Computers in Simulation 1 Mathematika 1 Monatshefte für Mathematik 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Theory and Decision 1 Combinatorica 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematica Hungarica 1 Extracta Mathematicae 1 Information and Computation 1 Journal of Automated Reasoning 1 Annals of Operations Research 1 International Journal of Foundations of Computer Science 1 Automation and Remote Control 1 SIAM Review 1 Stochastic Processes and their Applications 1 Expositiones Mathematicae 1 Mathematical Communications 1 Journal of Group Theory 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Nonlinear Science and Numerical Simulation 1 Lobachevskii Journal of Mathematics 1 Journal of Nonlinear Mathematical Physics 1 Logic and Logical Philosophy 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 Proceedings of the Steklov Institute of Mathematics 1 Complex Analysis and Operator Theory 1 Logic and Analysis 1 Groups, Geometry, and Dynamics 1 Logical Methods in Computer Science 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Topology and Analysis 1 Science China. Mathematics 1 Annals of Finance 1 Quantum Studies: Mathematics and Foundations 1 Sahand Communications in Mathematical Analysis 1 Graduate Journal of Mathematics all top 5 Cited in 39 Fields 206 Mathematical logic and foundations (03-XX) 36 Real functions (26-XX) 29 History and biography (01-XX) 23 Measure and integration (28-XX) 18 General topology (54-XX) 14 General and overarching topics; collections (00-XX) 12 Functional analysis (46-XX) 11 Probability theory and stochastic processes (60-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 10 Computer science (68-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Combinatorics (05-XX) 8 Group theory and generalizations (20-XX) 8 Dynamical systems and ergodic theory (37-XX) 6 Numerical analysis (65-XX) 5 Number theory (11-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Operations research, mathematical programming (90-XX) 3 Topological groups, Lie groups (22-XX) 3 Sequences, series, summability (40-XX) 3 Operator theory (47-XX) 3 Systems theory; control (93-XX) 2 Category theory; homological algebra (18-XX) 2 Potential theory (31-XX) 2 Ordinary differential equations (34-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Mechanics of particles and systems (70-XX) 1 Field theory and polynomials (12-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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