Chong, Chi Tat; Wang, Wei; Yang, Yue Conservation strength of the Infinite pigeonhole principle for trees. (English) Zbl 07871048 Isr. J. Math. 260, No. 1, 341-364 (2024). MSC: 03Bxx 03Fxx 03Dxx × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Marker, David An invitation to mathematical logic. (English) Zbl 07814037 Graduate Texts in Mathematics 301. Cham: Springer (ISBN 978-3-031-55367-7/hbk; 978-3-031-55370-7/pbk; 978-3-031-55368-4/ebook). xviii, 357 p. (2024). MSC: 03-01 03Cxx 03Dxx 03Fxx × Cite Format Result Cite Review PDF Full Text: DOI
Matthews, Richard; Rathjen, Michael Constructing the constructible universe constructively. (English) Zbl 07785165 Ann. Pure Appl. Logic 175, No. 3, Article ID 103392, 25 p. (2024). MSC: 03E45 03E70 03D65 03E10 03F55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fiori-Carones, M. Variations of statement, variations of strength. The case of the Rival-Sands theorems. (English) Zbl 07798371 J. Math. Sci., New York 275, No. 1, 1-15 (2023). MSC: 03Dxx 03Fxx 03Bxx × Cite Format Result Cite Review PDF Full Text: DOI
Tachikawa, Yuji Undecidable problems in quantum field theory. (English) Zbl 07738885 Int. J. Theor. Phys. 62, No. 9, Paper No. 199, 13 p. (2023). MSC: 03Dxx 03Bxx 03Fxx × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liu, Lu The coding power of a product of partitions. (English) Zbl 07720434 Isr. J. Math. 255, No. 2, 645-683 (2023). MSC: 03Dxx 03Bxx 03Fxx × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shore, Richard A. Almost theorems of hyperarithmetic analysis. (English) Zbl 1525.03056 J. Symb. Log. 88, No. 2, 664-696 (2023). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03F35 03D55 05C63 03F65 03D80 05C38 × Cite Format Result Cite Review PDF Full Text: DOI
Koswara, Ivan; Pogudin, Gleb; Selivanova, Svetlana; Ziegler, Martin Bit-complexity of classical solutions of linear evolutionary systems of partial differential equations. (English) Zbl 07667582 J. Complexity 76, Article ID 101727, 32 p. (2023). MSC: 68Qxx 03Dxx 03Fxx × Cite Format Result Cite Review PDF Full Text: DOI
Avigad, Jeremy Mathematical logic and computation. (English) Zbl 1524.03001 Cambridge: Cambridge University Press (ISBN 978-1-108-47875-5/hbk; 978-1-108-77875-6/ebook). xii, 513 p. (2023). MSC: 03-01 03Dxx 03Fxx × Cite Format Result Cite Review PDF Full Text: DOI
Savitskii, I. V. On the coincidence of complexity classes BPC and \(\text{TC}^0 \). (English. Russian original) Zbl 07688769 Mosc. Univ. Comput. Math. Cybern. 46, No. 4, 204-214 (2022); translation from Vestn. Mosk. Univ., Ser. XV 2022, No. 4, 36-45 (2022). MSC: 68Qxx 03Dxx 03Fxx × Cite Format Result Cite Review PDF Full Text: DOI
Monin, Benoît; Patey, Ludovic Computability. Randomness, reverse mathematics and hypercomputability. (Calculabilité. Aléatoire, mathématiques à rebours et hypercalculabilité.) (French) Zbl 1516.03001 Tableau Noir 107. Paris: Calvage et Mounet (ISBN 978-2-916352-96-1/hbk). xxii, 828 p. (2022). Reviewer: Jeffry L. Hirst (Boone) MSC: 03-01 68-01 03Dxx 03B10 03C07 03B30 03F35 03F40 03D80 68Q04 68Q30 × Cite Format Result Cite Review PDF
Sato, Kentaro Bounded inductive dichotomy: separation of open and clopen determinacies with finite alternatives in constructive contexts. (English) Zbl 07541618 Arch. Math. Logic 61, No. 3-4, 399-435 (2022). MSC: 03D70 03E65 03F35 03F55 03D30 03F50 × Cite Format Result Cite Review PDF Full Text: DOI
Mainzer, Klaus (ed.); Schuster, Peter (ed.); Schwichtenberg, Helmut (ed.) Proof and computation II. From proof theory and univalent mathematics to program extraction and verification. Based on the international autumn school “Proof and computation”, September 20–26, 2019. (English) Zbl 1486.03009 Hackensack, NJ: World Scientific (ISBN 978-981-12-3647-1/hbk; 978-981-12-3649-5/ebook). xvi, 408 p. (2022). MSC: 03-06 03Dxx 03F65 03B70 00B25 × Cite Format Result Cite Review PDF Full Text: DOI
Brattka, Vasco (ed.); Greenberg, Noam (ed.); Kalimullin, Iskander (ed.); Soskova, Mariya (ed.) Computability theory. Abstracts from the workshop held April 25 – May 1, 2021 (hybrid meeting). (English) Zbl 1506.00048 Oberwolfach Rep. 18, No. 2, 1149-1190 (2021). MSC: 00B05 00B25 03-06 68-06 03Dxx 03B30 03C57 03Fxx 68Qxx × Cite Format Result Cite Review PDF Full Text: DOI
Dzhafarov, Damir; Flood, Stephen; Solomon, Reed; Westrick, Linda Effectiveness for the dual Ramsey theorem. (English) Zbl 1508.03078 Notre Dame J. Formal Logic 62, No. 3, 455-490 (2021). Reviewer: Iosif Petrakis (München) MSC: 03D80 03B30 05C55 05D10 03F60 03F35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fujiwara, Makoto Weihrauch and constructive reducibility between existence statements. (English) Zbl 1535.03294 Computability 10, No. 1, 17-30 (2021). MSC: 03F65 03B30 03D30 03F35 × Cite Format Result Cite Review PDF Full Text: DOI
Brattka, Vasco; Gherardi, Guido Completion of choice. (English) Zbl 1462.03019 Ann. Pure Appl. Logic 172, No. 3, Article ID 102914, 31 p. (2021). Reviewer: Jeffry L. Hirst (Boone) MSC: 03D78 03B30 03D30 03F60 03F35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fujiwara, Makoto; Kawai, Tatsuji Characterising Brouwer’s continuity by bar recursion on moduli of continuity. (English) Zbl 1496.03254 Arch. Math. Logic 60, No. 1-2, 241-263 (2021). Reviewer: Danko Ilik (Paris) MSC: 03F55 03B30 03F35 03F50 03F10 × Cite Format Result Cite Review PDF Full Text: DOI
Normann, Dag; Sanders, Sam Open sets in computability theory and reverse mathematics. (English) Zbl 1472.03012 J. Log. Comput. 30, No. 8, 1639-1679 (2020). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03D65 03F35 03D80 03F60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dzhafarov, Damir D.; Goh, Jun Le; Hirschfeldt, Denis R.; Patey, Ludovic; Pauly, Arno Ramsey’s theorem and products in the Weihrauch degrees. (English) Zbl 1485.03026 Computability 9, No. 2, 85-110 (2020). MSC: 03B30 03D78 03D30 05D10 03F60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hirst, Jeffry L.; Mummert, Carl Using Ramsey’s theorem once. (English) Zbl 1475.03071 Arch. Math. Logic 58, No. 7-8, 857-866 (2019). Reviewer: Emil Jeřábek (Praha) MSC: 03B30 03F35 03F50 03D30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Brattka, Vasco; Le Roux, Stéphane; Miller, Joseph S.; Pauly, Arno Connected choice and the Brouwer fixed point theorem. (English) Zbl 1484.03130 J. Math. Log. 19, No. 1, Article ID 1950004, 46 p. (2019). MSC: 03F60 03D30 03D78 03B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Centrone, Stefania (ed.); Negri, Sara (ed.); Sarikaya, Deniz (ed.); Schuster, Peter M. (ed.) Mathesis universalis, computability and proof. Based on the Humboldt-Kolleg “Proof theory as mathesis universalis”, held at the German-Italian Centre for European Excellence, Villa Vigoni, Loveno di Menaggio, Como, Italy, July 24–28, 2017. (English) Zbl 1431.03011 Synthese Library 412. Cham: Springer (ISBN 978-3-030-20446-4/hbk; 978-3-030-20447-1/ebook). x, 374 p. (2019). MSC: 03-06 01-06 03A05 03Dxx 03F60 00A30 00B25 × Cite Format Result Cite Review PDF Full Text: DOI
Kawai, Tatsuji Representing definable functions of \(\mathrm{HA}^{\omega}\) by neighbourhood functions. (English) Zbl 1461.03057 Ann. Pure Appl. Logic 170, No. 8, 891-909 (2019). MSC: 03F55 03F50 03F10 03D65 03F30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fujiwara, Makoto; Kawai, Tatsuji Equivalence of bar induction and bar recursion for continuous functions with continuous moduli. (English) Zbl 1459.03091 Ann. Pure Appl. Logic 170, No. 8, 867-890 (2019). MSC: 03F55 03F35 03F10 03B30 03F50 × Cite Format Result Cite Review PDF Full Text: DOI
Mainzer, Klaus Proof and computation. (English) Zbl 07909424 Mainzer, Klaus (ed.) et al., Proof and computation. Digitization in mathematics, computer science, and philosophy. Based on the international autumn school “Proof and computation”, Fischbachau, Germany, October 3–8, 2016. Hackensack, NJ: World Scientific. 1-52 (2018). MSC: 03D10 03D25 03D65 03D78 03F50 03B30 × Cite Format Result Cite Review PDF Full Text: DOI
Sen, Yang Whitehead’s problem and reverse mathematics. (English) Zbl 1405.03033 Isr. J. Math. 228, No. 1, 455-512 (2018). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03F35 03D80 20K99 × Cite Format Result Cite Review PDF Full Text: DOI
Jäger, Gerhard; Rosebrock, Timotej; Kentaro, Sato Truncation and semi-decidability notions in applicative theories. (English) Zbl 1475.03074 J. Symb. Log. 83, No. 3, 967-990 (2018). Reviewer: Reinhard Kahle (Lisboa) MSC: 03B40 03D25 03D75 03F50 × Cite Format Result Cite Review PDF Full Text: DOI Link
Mainzer, Klaus (ed.); Schuster, Peter (ed.); Schwichtenberg, Helmut (ed.) Proof and computation. Digitization in mathematics, computer science, and philosophy. Based on the international autumn school “Proof and computation”, Fischbachau, Germany, October 3–8, 2016. (English) Zbl 1400.03005 Hackensack, NJ: World Scientific (ISBN 978-981-3270-93-0/hbk; 978-981-3270-95-4/ebook). viii, 291 p. (2018). MSC: 03-06 03Dxx 03F65 03B70 00B25 × Cite Format Result Cite Review PDF Full Text: DOI
Bauer, Andrej On fixed-point theorems in synthetic computability. (English) Zbl 1403.03076 Tbil. Math. J. 10, No. 3, 167-181 (2017). MSC: 03D75 54H25 03F65 × Cite Format Result Cite Review PDF Full Text: DOI Backlinks: MO
Brattka, Vasco; Cettolo, Andrea; Gherardi, Guido; Marcone, Alberto; Schröder, Matthias Addendum to: “The Bolzano-Weierstrass theorem is the jump of weak Kőnig’s lemma”. (English) Zbl 1403.03127 Ann. Pure Appl. Logic 168, No. 8, 1605-1608 (2017). MSC: 03F60 03B30 03D30 03E15 × Cite Format Result Cite Review PDF Full Text: DOI
Greenberg, Noam; Melnikov, Alexander Proper divisibility in computable rings. (English) Zbl 1370.03021 J. Algebra 474, 180-212 (2017). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03D45 13G05 03D80 16U10 03F35 × Cite Format Result Cite Review PDF Full Text: DOI
Sanders, Sam The computational content of nonstandard analysis. (English) Zbl 1486.03128 Kohlenbach, Ulrich (ed.) et al., Proceedings of the sixth international workshop on classical logic and computation, CL&C 2016, Porto, Portugal, June 23, 2016. Waterloo: Open Publishing Association (OPA). Electron. Proc. Theor. Comput. Sci. (EPTCS) 213, 24-40 (2016). MSC: 03H05 03B30 03E70 03F60 03D65 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Day, Adam R. On the strength of two recurrence theorems. (English) Zbl 1368.03016 J. Symb. Log. 81, No. 4, 1357-1374 (2016). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 54H20 03D30 03F35 03F60 37B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Escardó, Martín; Xu, Chuangjie A constructive manifestation of the Kleene-Kreisel continuous functionals. (English) Zbl 1402.03020 Ann. Pure Appl. Logic 167, No. 9, 770-793 (2016). MSC: 03B15 03F50 03C90 03D65 × Cite Format Result Cite Review PDF Full Text: DOI
Petrakis, Iosif Limit spaces with approximations. (English) Zbl 1432.03083 Ann. Pure Appl. Logic 167, No. 9, 737-752 (2016). MSC: 03D75 03D80 03F60 × Cite Format Result Cite Review PDF Full Text: DOI
Le Roux, Stéphane; Pauly, Arno Finite choice, convex choice and finding roots. (English) Zbl 1448.03052 Log. Methods Comput. Sci. 11, No. 4, Paper No. 6, 30 p. (2015). MSC: 03F60 03D30 03D78 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fujiwara, Makoto Intuitionistic provability versus uniform provability in \(\mathsf{RCA}\). (English) Zbl 1461.03009 Beckmann, Arnold (ed.) et al., Evolving computability. 11th conference on computability in Europe, CiE 2015, Bucharest, Romania, June 29 – July 3, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9136, 186-195 (2015). MSC: 03B30 03D30 03F55 03F45 03F60 × Cite Format Result Cite Review PDF Full Text: DOI
Dowek, Gilles Computation, proof, machine. Mathematics enters a new age. Translated from the French by Pierre Guillot and Marion Roman. (English) Zbl 1318.01002 Cambridge: Cambridge University Press (ISBN 978-0-521-13377-7/pbk; 978-0-521-11801-9/hbk). viii, 152 p. (2015). MSC: 01-02 03-03 03B35 03B40 03B70 03Dxx 03Fxx 68-XX 68-02 68-03 68N18 68Qxx 68T15 × Cite Format Result Cite Review PDF
Normann, Dag The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems. (English) Zbl 1448.03053 Log. Methods Comput. Sci. 11, No. 1, Paper No. 8, 27 p. (2015). MSC: 03F60 03D65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kreuzer, Alexander P. From Bolzano-Weierstrass to Arzelà-Ascoli. (English) Zbl 1331.03016 Math. Log. Q. 60, No. 3, 177-183 (2014). Reviewer: Jeffry L. Hirst (Boone) MSC: 03B30 03F35 03D30 03F60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Higuchi, K.; Kihara, T. Inside the Muchnik degrees. I: Discontinuity, learnability and constructivism. (English) Zbl 1315.03071 Ann. Pure Appl. Logic 165, No. 5, 1058-1114 (2014). MSC: 03D30 03D78 03E15 03F60 68Q32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shore, Richard A. Reverse mathematics, countable and uncountable. (English) Zbl 1329.03046 Greenberg, Noam (ed.) et al., Effective mathematics of the uncountable. Cambridge: Cambridge University Press; Ithaca, NY: Association for Symbolic Logic (ASL) (ISBN 978-1-107-01451-0/hbk; 978-1-139-02859-2/ebook). Lecture Notes in Logic 41, 150-163 (2013). MSC: 03B30 03D45 03D60 03D80 03F35 03F65 × Cite Format Result Cite Review PDF
Ilik, Danko An interpretation of the Sigma-2 fragment of classical Analysis in System T. arXiv:1301.5089 Preprint, arXiv:1301.5089 [math.LO] (2013). MSC: 03F25 03F10 03F60 03B30 03B20 03E25 03D65 68N15 × Cite Format Result Cite Full Text: arXiv OA License
Velupillai, K. Vela Reflections on mathematical economics in the algorithmic mode. (English) Zbl 1283.91037 New Math. Nat. Comput. 8, No. 1, 139-152 (2012). MSC: 91B02 03D80 03F60 03H10 26E35 91B99 × Cite Format Result Cite Review PDF Full Text: DOI
Zambelli, Stefano Computable economics: reconstructing the nonconstructive. (English) Zbl 1283.91038 New Math. Nat. Comput. 8, No. 1, 113-122 (2012). MSC: 91B02 03D78 03D80 03F60 91B99 × Cite Format Result Cite Review PDF Full Text: DOI
Kinsella, Stephen Blueprint for an algorithmic economics. (English) Zbl 1283.91034 New Math. Nat. Comput. 8, No. 1, 101-111 (2012). MSC: 91B02 03D78 03D80 03F60 91B50 91B64 × Cite Format Result Cite Review PDF Full Text: DOI
Kreuzer, Alexander P. On the strength of weak compactness. (English) Zbl 1270.03128 Computability 1, No. 2, 171-179 (2012). Reviewer: Iris Loeb (Amsterdam) MSC: 03F60 03D80 03B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kreuzer, Alexander P. Proof mining and combinatorics. Program extraction for Ramsey’s theorem for pairs. (English) Zbl 1262.03003 Darmstadt: TU Darmstadt, Fachbereich Mathematik (Diss.). 147 p. (2012). Reviewer: Laurenţiu Leuştean (Bucureşti) MSC: 03-02 03B30 03D80 03F10 03F35 03F60 05D10 × Cite Format Result Cite Review PDF Full Text: Link
Berger, Ulrich (ed.); Brattka, Vasco (ed.); Morozov, Andrei S. (ed.); Spreen, Dieter (ed.) Special issue: Selected papers based on the presentations at the workshop ‘Continuity, computability, constructivity: from logic to algorithms’, Cologne, Germany, July 2009. (English) Zbl 1282.03005 Ann. Pure Appl. Logic 163, No. 8, 973-1139 (2012). MSC: 03-06 03Dxx 03Fxx 00B25 × Cite Format Result Cite Review PDF
Beckmann, Arnold (ed.); Löwe, Benedikt (ed.) Special issue: Computability in Europe 2008. Selected papers based on the presentations at the 4th conference, CiE 2008, ‘Logic and theory of algorithms’, Athens, Greece, June 15–20, 2008. (English) Zbl 1282.03004 J. Log. Comput. 22, No. 2, 163-350 (2012). MSC: 03-06 68-06 03Dxx 03Fxx 68Qxx 00B25 × Cite Format Result Cite Review PDF
Brattka, Vasco; Gherardi, Guido; Marcone, Alberto The Bolzano-Weierstrass theorem is the jump of weak Kőnig’s lemma. (English) Zbl 1245.03097 Ann. Pure Appl. Logic 163, No. 6, 623-655 (2012); addendum ibid. 168, No. 8, 1605-1608 (2017). Reviewer: Iris Loeb (Christchurch) MSC: 03F60 03B30 03D30 03E15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Backlinks: MO
Ferreira, Fernando (ed.); Hyland, Martin (ed.); Löwe, Benedikt (ed.); Mayordomo, Elvira (ed.) Special issue: Computability in Europe 2010. Selected papers based on the presentations at the 6th CiE meeting on programs, proofs, processes, Ponta Delgada, Portugal, June 30 – July 4, 2010. (English) Zbl 1250.03006 Ann. Pure Appl. Logic 163, No. 6, 621-742 (2012). MSC: 03-06 03Dxx 03Fxx 00B25 × Cite Format Result Cite Review PDF
Dowek, Gilles The metamorphoses of the calculus. An amazing history of mathematics. Reprint of the 2007 edition. (Les métamorphoses du calcul. Une étonnante histoire de mathématiques.) (French) Zbl 1360.01012 Poche. Paris: Éditions Le Pommier (ISBN 978-2-7465-0561-2/pbk). 224 p. (2011). MSC: 01-02 03-03 03B35 03B40 03B70 03Dxx 03Fxx 68-02 68-03 68N18 68Qxx 68T15 × Cite Format Result Cite Review PDF
Brattka, Vasco; Gherardi, Guido Effective choice and boundedness principles in computable analysis. (English) Zbl 1226.03062 Bull. Symb. Log. 17, No. 1, 73-117 (2011). Reviewer: Iris Loeb (Christchurch) MSC: 03F60 03B30 03D30 03D45 03E15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Brattka, Vasco; Gherardi, Guido Weihrauch degrees, omniscience principles and weak computability. (English) Zbl 1222.03071 J. Symb. Log. 76, No. 1, 143-176 (2011). Reviewer: Iris Loeb (Christchurch) MSC: 03F60 03B30 03D30 03D45 03E15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Huber, Simon; Karádais, Basil A.; Schwichtenberg, Helmut Towards a formal theory of computability. (English) Zbl 1245.03064 Schindler, Ralf (ed.), Ways of proof theory. Collected papers by speakers of the colloquium and workshop held on the occasion of the retirement of Wolfram Pohlers, July 17–19, 2008, Münster, Germany. Frankfurt am Main: Ontos Verlag (ISBN 978-3-86838-087-3/hbk). Ontos Mathematical Logic 2, 257-282 (2010). MSC: 03D65 03F65 × Cite Format Result Cite Review PDF
Bauer, Andrej; Kavkler, Iztok A constructive theory of continuous domains suitable for implementation. (English) Zbl 1169.06005 Ann. Pure Appl. Logic 159, No. 3, 251-267 (2009). Reviewer: Dieter Spreen (Siegen) MSC: 06B35 03D65 03F60 03B70 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Yatao; Grubba, Tanja On computably locally compact Hausdorff spaces. (English) Zbl 1159.03044 Math. Struct. Comput. Sci. 19, No. 1, 101-117 (2009). MSC: 03F60 03F65 03D80 × Cite Format Result Cite Review PDF Full Text: DOI
Steen, S. W. P. Mathematical logic with special reference to the natural numbers. Paperback reprint of the 1972 edition. (English) Zbl 1156.03002 Cambridge: Cambridge University Press (ISBN 978-0-521-09058-2/pbk). xvi, 638 p. (2008). MSC: 03-01 03B05 03B10 03B25 03Cxx 03Dxx 03Fxx × Cite Format Result Cite Review PDF
Berger, Ulrich Classical truth in higher types. (English) Zbl 1140.03037 Math. Log. Q. 54, No. 3, 240-246 (2008). MSC: 03F10 03B15 03D65 03E25 03F50 × Cite Format Result Cite Review PDF Full Text: DOI
Schwichtenberg, Helmut Recursion on the partial continuous functionals. (English) Zbl 1137.03035 Dimitracopoulos, Costas (ed.) et al., Logic colloquium 2005. Proceedings of the annual European summer meeting of the Association for Symbolic Logic (ASL), Athens, Greece, July 28–August 3, 2005. Cambridge: Cambridge University Press; Urbana, IL: Association for Symbolic Logic (ASL) (ISBN 978-0-521-88425-9/hbk). Lecture Notes in Logic 28, 173-201 (2008). MSC: 03F65 03D65 03D75 × Cite Format Result Cite Review PDF
Dowek, Gilles The metamorphoses of the calculus. An amazing history of mathematics. (Les métamorphoses du calcul. Une étonnante histoire de mathématiques.) (French) Zbl 1161.01001 Paris: Éditions Le Pommier (ISBN 978-2-7465-0324-3/pbk). 224 p. (2007). Reviewer: Radoslav M. Dimitrić (Uniontown) MSC: 01-02 03-03 03B35 03B40 03B70 03Dxx 03Fxx 68-02 68-03 68N18 68Qxx 68T15 × Cite Format Result Cite Review PDF
Bauer, Andrej First steps in synthetic computability theory. (English) Zbl 1273.03144 Escardó, M. (ed.) et al., Proceedings of the 21st annual conference on mathematical foundations of programming semantics (MFPS XXI), University of Birmingham, Birmingham, UK, May 18–21, 2005. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 155, 5-31 (2006). MSC: 03D75 03F65 03G30 68Q01 × Cite Format Result Cite Review PDF Full Text: Link
Simonsen, Jakob G. On local non-compactness in recursive mathematics. (English) Zbl 1095.03034 Math. Log. Q. 52, No. 4, 323-330 (2006). MSC: 03D80 03F60 54E35 × Cite Format Result Cite Review PDF Full Text: DOI
Calude, Cristian S.; Rudeanu, Sergiu Proving as a computable procedure. (English) Zbl 1091.03029 Fundam. Inform. 64, No. 1-4, 43-52 (2005). Reviewer: Roman Murawski (Poznań) MSC: 03F99 03D99 × Cite Format Result Cite Review PDF
Nakata, Masahiro; Hayashi, Susumu A limiting first order realizability interpretation. (English) Zbl 1003.03049 Sci. Math. Jpn. 55, No. 3, 567-580 (2002). MSC: 03F50 03B70 03D80 03F65 68Q32 68Q60 68T05 × Cite Format Result Cite Review PDF
Cenzer, Douglas; Jockusch, Carl G. jun. \(\Pi_1^0\) classes – structure and applications. (English) Zbl 0962.03040 Cholak, Peter A. (ed.) et al., Computability theory and its applications. Current trends and open problems. Proceedings of a 1999 AMS-IMS-SIAM joint summer research conference, Boulder, CO, USA, June 13-17, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 257, 39-59 (2000). MSC: 03D80 03D30 03D25 03C62 03E15 03F35 03F60 × Cite Format Result Cite Review PDF
Epstein, Richard L.; Carnielli, Walter A. Computability. Computable functions, logic, and the foundations of mathematics. With “Computability and undecidability—a timeline. The story of the development of computable functions and the undecidability of arithmetic to 1970” by Richard L. Epstein. 2nd ed. (English) Zbl 0951.03001 Belmont, CA: Wadsworth/Thomson Learning. 299 p., 38 p. (2000). Reviewer: B.Boričić (Beograd) MSC: 03-01 03Dxx 00A30 00A35 03Fxx 03A05 × Cite Format Result Cite Review PDF
Rathjen, Michael Explicit mathematics with the monotone fixed point principle II: Models. (English) Zbl 0930.03093 J. Symb. Log. 64, No. 2, 517-550 (1999). Reviewer: B.Boričić (Beograd) MSC: 03F50 03F35 03F65 × Cite Format Result Cite Review PDF Full Text: DOI
Murawski, Roman The contribution of Polish logicians to recursion theory. (English) Zbl 1018.03005 Kijania-Placek, Katarzyna (ed.) et al., The Lvov-Warsaw school and contemporary philosophy. Papers from the conference, Lviv (Lvov), Ukraine, November 15-17, 1995 and Warsaw, Poland, November 19-21, 1995. Dordrecht: Kluwer Academic Publishers. Synth. Libr. 273, 265-282 (1998). Reviewer: Roman Murawski (Poznań) MSC: 03-03 03Dxx 01A60 × Cite Format Result Cite Review PDF
Takasaki, Kanehisa Differential equations and computability. (Japanese) Zbl 0937.03070 RIMS Kokyuroku 1020, 39-62 (1997). MSC: 03F60 03D45 03D80 03H05 34A12 26E40 35L05 × Cite Format Result Cite Review PDF
Glaß, Thomas; Rathjen, Michael; Schlüter, Andreas On the proof-theoretic strength of monotone induction in explicit mathematics. (English) Zbl 0877.03027 Ann. Pure Appl. Logic 85, No. 1, 1-46 (1997). Reviewer: A.Cantini (Firenze) MSC: 03F50 03F35 03F25 03D60 03D70 × Cite Format Result Cite Review PDF Full Text: DOI
Odifreddi, Piergiorgio (ed.) Kreiseliana: about and around Georg Kreisel. (English) Zbl 0894.03002 Wellesley, MA: A K Peters. xiii, 495 p. (1996). Reviewer: V.Peckhaus (Erlangen) MSC: 03-03 01A70 01A60 01-02 03-02 00B15 03A05 03F50 × Cite Format Result Cite Review PDF
Sacks, Gerald E. Kreisel, generalized recursion theory and me. (English) Zbl 0895.01007 Odifreddi, Piergiorgio (ed.), Kreiseliana: about and around Georg Kreisel. Wellesley, MA: A K Peters. 103-106 (1996). Reviewer: V.Peckhaus (Erlangen) MSC: 01A70 03-03 03D60 × Cite Format Result Cite Review PDF
Schwichtenberg, Helmut Density and choice for total continuous functionals. (English) Zbl 0901.03039 Odifreddi, Piergiorgio (ed.), Kreiseliana: about and around Georg Kreisel. Wellesley, MA: A K Peters. 335-362 (1996). Reviewer: V.Peckhaus (Erlangen) MSC: 03F50 03F35 03-03 03D65 01A60 × Cite Format Result Cite Review PDF
Cenzer, Douglas; Remmel, Jeffrey Feasible graphs and colorings. (English) Zbl 0827.03037 Math. Log. Q. 41, No. 3, 327-352 (1995). MSC: 03F65 05C15 03D45 03D15 03D80 68Q15 × Cite Format Result Cite Review PDF Full Text: DOI
Schlüter, Andreas A theory of rules for enumerated classes of functions. (English) Zbl 0823.03005 Arch. Math. Logic 34, No. 1, 47-63 (1995). Reviewer: V.Ya.Kreinovich (El Paso) MSC: 03B40 03D80 03F50 03F65 × Cite Format Result Cite Review PDF Full Text: DOI
Hummel, Tamara Lakins Effective versions of Ramsey’s theorem: Avoiding the cone above 0’. (English) Zbl 0815.03028 J. Symb. Log. 59, No. 4, 1301-1325 (1994). Reviewer: W.I.Gasarch (College Park) MSC: 03D25 03D30 03F65 × Cite Format Result Cite Review PDF Full Text: DOI
Constable, Robert L.; Smith, Scott F. Computational foundations of basic recursive function theory. (English) Zbl 0798.03046 Theor. Comput. Sci. 121, No. 1-2, 89-112 (1993). Reviewer: H.B.Marandjian (Erevan) MSC: 03D75 03F65 03B35 × Cite Format Result Cite Review PDF Full Text: DOI Link OA License
Smullyan, Raymond M. Recursion theory for metamathematics. (English) Zbl 0796.03003 Oxford Logic Guides. 22. New York: Oxford University Press. xiv, 163 p. (1993). Reviewer: A.M.Coyne (Asheville) MSC: 03-02 03D99 03D35 03F99 × Cite Format Result Cite Review PDF
Weihrauch, Klaus A simple and powerful approach for studying constructivity, computability, and complexity. (English) Zbl 1434.03114 Myers, J. Paul jun. (ed.) et al., Constructivity in computer science. Summer symposium, San Antonio, TX, June 19–22, 1991. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 613, 228-246 (1992). MSC: 03D75 03F65 × Cite Format Result Cite Review PDF Full Text: DOI
Crole, Roy L.; Pitts, Andrew M. New foundations for fixpoint computations: FIX-hyperdoctrines and the FIX-logic. (English) Zbl 0763.03031 Inf. Comput. 98, No. 2, 171-210 (1992). MSC: 03F99 03D65 68Q55 03B40 18D15 18C15 × Cite Format Result Cite Review PDF Full Text: DOI
Di Paola, Robert A.; Montagna, Franco Some properties of the syntactic p-recursion categories generated by consistent, recursively enumerable extensions of Peano arithmetic. (English) Zbl 0745.03037 J. Symb. Log. 56, No. 2, 643-660 (1991). Reviewer: P.Bankston MSC: 03D75 18B99 03F99 × Cite Format Result Cite Review PDF Full Text: DOI
Takahashi, Shuzo Monotone inductive definitions in a constructive theory of functions and classes. (English) Zbl 0665.03037 Ann. Pure Appl. Logic 42, No. 3, 255-297 (1989). Reviewer: V.Yu.Sazonov MSC: 03D70 03F65 03D75 × Cite Format Result Cite Review PDF Full Text: DOI
Calude, Cristian; Vaida, Dragoş Languages, effectivity and constructive mathematics. (English) Zbl 0667.03036 Languages, logic, mathematical linguistics, Pap. 2nd Natl. Colloq., Braşov/Rom. 1988, 47-57 (1988). Reviewer: C.Calude MSC: 03D80 03F65 × Cite Format Result Cite Review PDF
Scedrov, Andre Kleene computable functionals and the higher order existence property. (English) Zbl 0647.03048 J. Pure Appl. Algebra 52, No. 3, 313-320 (1988). Reviewer: P.Bankston MSC: 03F35 03D65 18B25 03G30 03F55 × Cite Format Result Cite Review PDF Full Text: DOI
Demuth, Osvald Remarks on the structure of tt-degrees based on constructive measure theory. (English) Zbl 0646.03039 Commentat. Math. Univ. Carol. 29, No. 2, 233-247 (1988). MSC: 03D30 28A05 03F65 03D25 × Cite Format Result Cite Review PDF Full Text: EuDML
Demuth, Osvald Reducibilities of sets based on constructive functions of a real variable. (English) Zbl 0646.03038 Commentat. Math. Univ. Carol. 29, No. 1, 143-156 (1988). Reviewer: B.van Rootselaar MSC: 03D30 03F65 × Cite Format Result Cite Review PDF Full Text: EuDML
Buchholz, Wilfried Induktive Definitionen und Dilatoren. (Inductive definitions and dilators). (German) Zbl 0642.03034 Arch. Math. Logic 27, No. 1, 51-60 (1988). Reviewer: W.Buchholz MSC: 03F99 03D70 03D60 × Cite Format Result Cite Review PDF Full Text: DOI
Paulson, Lawrence C. Logic and computation. Interactive proof with Cambridge LCF. (English) Zbl 0645.68041 Cambridge Tracts in Theoretical Computer Science, 2. Cambridge etc.: Cambridge University Press. XIII, 302 p.; Ł 27.50; $ 34.50 (1987). Reviewer: J.-J.Ch.Meyer MSC: 68Q65 03-01 68-01 03B10 03F99 03D99 18C10 03B40 × Cite Format Result Cite Review PDF Full Text: DOI
Weihrauch, Klaus; Kreitz, Christoph Representations of the real numbers and of the open subsets of the set of real numbers. (English) Zbl 0643.03041 Ann. Pure Appl. Logic 35, 247-260 (1987). Reviewer: K.Weihrauch MSC: 03F60 03F65 03D45 03D65 × Cite Format Result Cite Review PDF Full Text: DOI
Howard, William The use of ordinals in the constructive foundations of mathematics. (English) Zbl 0623.03052 Logic, methodology and philosophy of science VII, Proc. 7th Int. Congr., Salzburg 1983, Stud. Logic Found. Math. 114, 83-94 (1986). Reviewer: H.Pfeiffer MSC: 03F15 03F50 03F35 03F10 03F05 × Cite Format Result Cite Review PDF
Gurevič, Reuben Transcendental numbers and eventual dominance of exponential functions. (English) Zbl 0621.03029 Bull. Lond. Math. Soc. 18, 560-570 (1986). Reviewer: P.Clote MSC: 03D30 03F99 × Cite Format Result Cite Review PDF Full Text: DOI
Hauck, Jürgen Ein Kriterium für die konstruktive Lösbarkeit der Differentialgleichung \(y'=f(x,y)\). (German) Zbl 0553.03037 Z. Math. Logik Grundlagen Math. 31, 357-362 (1985). MSC: 03F65 34A99 03D60 × Cite Format Result Cite Review PDF Full Text: DOI
Kolmogorov, A. N.; Dragalin, A. G. Mathematical logic. Complementary chapters. Textbook. (Matematicheskaya logika. Dopolnitel’nye glavy. Uchebnoe posobie). (Russian) Zbl 0591.03002 Moskva: Izdatel’stvo Moskovskogo Universiteta. 120 p. R. 0.25 (1984). Reviewer: I.H.Bekker MSC: 03-01 03Dxx 03Exx 03Fxx 68W99 × Cite Format Result Cite Review PDF
Demuth, O. Arithmetic complexity of differentiation in constructive mathematics. (Russian) Zbl 0582.03049 Commentat. Math. Univ. Carol. 24, 301-316 (1983). MSC: 03F65 03D30 26A24 × Cite Format Result Cite Review PDF Full Text: EuDML
Soskov, I. N. Algorithmically complete algebraic systems. (Russian) Zbl 0531.03039 C. R. Acad. Bulg. Sci. 36, 729-731 (1983). MSC: 03F65 03D60 03D99 × Cite Format Result Cite Review PDF
Richman, Fred Church’s thesis without tears. (English) Zbl 0527.03036 J. Symb. Log. 48, 797-803 (1983). MSC: 03F65 03D75 03D20 × Cite Format Result Cite Review PDF Full Text: DOI
Yasugi, Mariko Definability in the abstract theory of integration. (English) Zbl 0524.03050 Comment. Math. Univ. St. Pauli 32, 137-161 (1983). MSC: 03F65 46S30 03D70 28A25 × Cite Format Result Cite Review PDF