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Found 121 Documents (Results 1–100)

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Koenigsmann, Jochen
Undecidability in number theory. (English) Zbl 1347.03081
Macpherson, H. Dugald (ed.) et al., Model theory in algebra, analysis and arithmetic. Cetraro, Italy 2012. Lectures of the CIME course, Cetraro, Italy, 2012. Heidelberg: Springer; Florence: Fondazione CIME (ISBN 978-3-642-54935-9/pbk; 978-3-642-54936-6/ebook). Lecture Notes in Mathematics 2111. CIME Foundation Subseries, 159-195 (2014).
MSC:  03D35 03F40 11U05
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\textit{J. Koenigsmann}, Lect. Notes Math. 2111, 159--195 (2014; Zbl 1347.03081)
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Taschner, Rudolf
The number that came from the cold. When mathematics becomes an adventure. (Die Zahl, die aus der Kälte kam. Wenn Mathematik zum Abenteuer wird.) (German) Zbl 1401.00010
München: Carl Hanser Verlag (ISBN 978-3-446-43683-1/hbk; 978-3-446-43649-7/ebook). 243 p. (2013).
Reviewer: Ulrich Knauer (Oldenburg)
MSC:  00A09 01A05 97A80 11A41 03F30 94A60
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\textit{R. Taschner}, Die Zahl, die aus der Kälte kam. Wenn Mathematik zum Abenteuer wird. München: Carl Hanser Verlag (2013; Zbl 1401.00010)
Berto, Francesco
Wittgenstein on incompleteness makes paraconsistent sense. (English) Zbl 1261.03019
Tanaka, Koji (ed.) et al., Paraconsistency. Logic and applications. Selected papers of the 4th world congress on paraconsistency, Melbourne, Australia, 2008. Berlin: Springer (ISBN 978-94-007-4437-0/hbk). Logic, Epistemology, and the Unity of Science 26, 257-276 (2013).
MSC:  03A05 03B53 03F40
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\textit{F. Berto}, Log. Epistemol. Unity Sci. 26, 257--276 (2013; Zbl 1261.03019)
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Ferreirós, José
The justification of set theory: between metaphysics and formal axiomatics. (La justification de la théorie des ensembles: entre métaphysique et axiomatique formelle.) (French) Zbl 1280.01006
Flament, Dominique (ed.) et al., Justifier en mathématiques. Paris: Éditions de la Maison des Sciences de l’Homme (ISBN 978-2-7351-1414-6/pbk). 255-335 (2011).
Reviewer: V. N. Saliĭ (Saratov)
MSC:  01A55 01A60 00A30 03A05 03-03
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\textit{J. Ferreirós}, in: Justifier en mathématiques. Paris: Éditions de la Maison des Sciences de l'Homme. 255--335 (2011; Zbl 1280.01006)
Isaacson, Daniel
Necessary and sufficient conditions for undecidability of the Gödel sentence and its truth. (English) Zbl 1259.03075
DeVidi, David (ed.) et al., Logic, mathematics, philosophy: vintage enthusiasms. Essays in honour of John L. Bell. Berlin: Springer (ISBN 978-94-007-0213-4/hbk; 978-94-007-0214-1/ebook). The Western Ontario Series in Philosophy of Science 75, 135-152 (2011).
MSC:  03F40 03B25
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\textit{D. Isaacson}, in: Logic, mathematics, philosophy: vintage enthusiasms. Essays in honour of John L. Bell. Berlin: Springer. 135--152 (2011; Zbl 1259.03075)
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Naas, Josef; Tutschke, Wolfgang
Great theorems and beautiful proofs in mathematics. Identity of the beautiful, the general and the applicable. 3rd corrected and expanded ed. (Große Sätze und schöne Beweise der Mathematik: Identität des Schönen, Allgemeinen, Anwendbaren.) (German) Zbl 1171.00002
Frankfurt am Main: Harri Deutsch (ISBN 978-3-8171-1822-9/pbk). vi, 204 p. (2009).
Reviewer: Franz Lemmermeyer (Jagstzell)
MSC:  00A05 00A35
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\textit{J. Naas} and \textit{W. Tutschke}, Große Sätze und schöne Beweise der Mathematik: Identität des Schönen, Allgemeinen, Anwendbaren. 3rd corrected and expanded ed. Frankfurt am Main: Harri Deutsch (2009; Zbl 1171.00002)
Bailly, Francis; Longo, Giuseppe
Phenomenology of incompleteness: From formal deductions to mathematics and physics. (English) Zbl 1189.03003
Lupacchini, Rossella (ed.) et al., Deduction, computation, experiment. Exploring the effectiveness of proof. Including papers from the workshop held at the University of Bologna, Bologna, Italy, April 3–4, 2007. Berlin: Springer (ISBN 978-88-470-0783-3/pbk). 243-271 (2008).
MSC:  03A05 00A30 00A79
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\textit{F. Bailly} and \textit{G. Longo}, in: Deduction, computation, experiment. Exploring the effectiveness of proof. Including papers from the workshop held at the University of Bologna, Bologna, Italy, April 3--4, 2007. Berlin: Springer. 243--271 (2008; Zbl 1189.03003)
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Sieg, Wilfried; Field, Clinton
Automated search for Gödel’s proofs. (English) Zbl 1191.03010
Lupacchini, Rossella (ed.) et al., Deduction, computation, experiment. Exploring the effectiveness of proof. Including papers from the workshop held at the University of Bologna, Bologna, Italy, April 3–4, 2007. Berlin: Springer (ISBN 978-88-470-0783-3/pbk). 117-140 (2008).
MSC:  03B35 68T15 68T20
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\textit{W. Sieg} and \textit{C. Field}, in: Deduction, computation, experiment. Exploring the effectiveness of proof. Including papers from the workshop held at the University of Bologna, Bologna, Italy, April 3--4, 2007. Berlin: Springer. 117--140 (2008; Zbl 1191.03010)
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Willard, Dan E.
The axiom system \(\mathrm{I}\Sigma_{0}\) manages to simultaneously obey and evade the Herbrandized version of the second incompleteness theorem. (English) Zbl 1262.03122
Mints, G. (ed.) et al., Proceedings of the 13th workshop on logic, language, information and computation (WoLLIC 2006), Stanford, CA, USA, July 18–21, 2006. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 165, 213-226 (2006).
MSC:  03F30 03F40
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\textit{D. E. Willard}, Electron. Notes Theor. Comput. Sci. 165, 213--226 (2006; Zbl 1262.03122)
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Facchini, Alessandro
“The House of Hilbert”: a very pretty building with neither a roof nor a floor. Model-theoretic analysis of a failed program. With a foreword by Denis Miéville. (“Maison Hilbert”: un très joli édifice sans toit ni sol. Analyse model-théorétique d’un échec.) (French) Zbl 1060.03004
Travaux de Logique. Centre de Recherches Sémiologiques 15. Neuchâtel: Université de Neuchâtel, Centre de Recherches Sémiologiques. xii, 81 p. (2003).
Reviewer: Roman Murawski (Poznań)
MSC:  03-02 03-03 03A05 00A30
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\textit{A. Facchini}, ``Maison Hilbert'': un très joli édifice sans toit ni sol. Analyse model-théorétique d'un échec. Neuchâtel: Université de Neuchâtel, Centre de Recherches Sémiologiques (2003; Zbl 1060.03004)
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
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\textit{R. L. Epstein} and \textit{W. A. Carnielli}, 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. Belmont, CA: Wadsworth/Thomson Learning (2000; Zbl 0951.03001)
Akimov, A. A.
On an axiom of predicate calculus from “Gödel’s incompleteness theorems” by R. Smullyan. (English. Russian original) Zbl 0954.03007
Mosc. Univ. Math. Bull. 54, No. 2, 41-43 (1999); translation from Vestn. Mosk. Univ., Ser. I 1999, No. 2, 60-62 (1999).
Reviewer: A. A. Martynyuk (Kyïv)
MSC:  03B10 03F30
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\textit{A. A. Akimov}, Mosc. Univ. Math. Bull. 54, No. 2, 60--62 (1999; Zbl 0954.03007); translation from Vestn. Mosk. Univ., Ser. I 1999, No. 2, 60--62 (1999)
Chaitin, Gregory J.
Number and randomness: Algorithmic information theory – New results on the foundations of mathematics. (English) Zbl 0915.03012
Driessen, Alfred (ed.) et al., Mathematical undecidability, quantum nonlocality and the question of the existence of God. Dordrecht: Kluwer Academic Publishers. 15-25 (1997).
Reviewer: V.Ya.Kreinovich (El Paso)
MSC:  03B30 68Q30 00A30 03D10
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\textit{G. J. Chaitin}, in: Mathematical undecidability, quantum nonlocality and the question of the existence of God. Dordrecht: Kluwer Academic Publishers. 15--25 (1997; Zbl 0915.03012)
Adamowicz, Zofia; Zbierski, Paweł
Logic of mathematics: a modern course of classical logic. (English) Zbl 0874.03003
Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs and Tracts. New York, NY: John Wiley & Sons (ISBN 0-471-06026-7/hbk). viii, 260 p. (1997).
Reviewer: B.Boričić (Beograd)
MSC:  03-01
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\textit{Z. Adamowicz} and \textit{P. Zbierski}, Logic of mathematics: a modern course of classical logic. New York, NY: John Wiley \& Sons (1997; Zbl 0874.03003)
Calude, Cristian; Campbell, Douglas I.; Svozil, Karl; Ştefǎnescu, Doru
Strong determinism vs. computability. (English) Zbl 0970.03021
DePauli-Schimanovich, Werner (ed.) et al., The foundational debate. Complexity and constructivity in mathematics and physics. Proceedings of the conference on the foundational debate: constructivity and complexity in logic, mathematics and physics, Vienna, Austria, September 1994. Dordrecht: Kluwer Academic Publishers. Vienna Circ. Inst. Yearb. 3, 115-131 (1995).
MSC:  03B30 68Q05 81P05 81P10 00A79
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\textit{C. Calude} et al., Vienna Circ. Inst. Yearb. 3, 115--131 (1995; Zbl 0970.03021)
Willard, Dan E.
Self-verifying axiom systems. (English) Zbl 0805.03053
Gottlob, Georg (ed.) et al., Computational logic and proof theory. 3rd Kurt Gödel Colloquium, KGC ’93, Brno, Czech Republic, August 24-27, 1993. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 713, 325-336 (1993).
MSC:  03F99 03F30
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\textit{D. E. Willard}, Lect. Notes Comput. Sci. 713, 325--336 (1993; Zbl 0805.03053)
Friedman, Harvey
The incompleteness phenomena. (English) Zbl 0929.03052
Browder, Felix E. (ed.), Mathematics into the twenty-first century. Proceedings of the AMS centennial symposium, Providence, RI, USA, August 8–12, 1988. Providence, RI: American Mathematical Society. Am. Math. Soc. Centen. Publ. 2, 49-84 (1992).
MSC:  03E35 03D35 03A05 03-02 03-01 03B30 03F35 03E30
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\textit{H. Friedman}, in: Mathematics into the twenty-first century. Proceedings of the AMS centennial symposium, Providence, RI, USA, August 8--12, 1988. Providence, RI: American Mathematical Society. 49--84 (1992; Zbl 0929.03052)
Murawski, Roman
Recursive functions and elements of metamathematics. Problems of completeness, decidability and Gödel’s theorems. (Funkcje rekurencyjne i elementy metamatematyki. Problemy zupełności, rozstrzygalności, twierdzenia Gödla.) (Polish) Zbl 0719.03001
Seria Matematyka, Uniwersytet Im. Adama Mickiewicza w Poznaniu, 11. Poznań: Wydawnictwo Naukowe Uniwersytetu Im. Adama Mickiewicza w Poznaniu. 186 p. (1990).
Reviewer: O.V.Belegradek (Kemerovo)
MSC:  03-01 03D20 03F30 03B25 03-03 03D10 03D35 03A05
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\textit{R. Murawski}, Funkcje rekurencyjne i elementy metamatematyki. Problemy zupełności, rozstrzygalności, twierdzenia Gödla (Polish). Poznań: Wydawnictwo Naukowe Uniwersytetu Im. Adama Mickiewicza w Poznaniu (1990; Zbl 0719.03001)
Naas, Josef; Tutschke, Wolfgang
Große Sätze und schöne Beweise der Mathematik: Identität des Schönen, Allgemeinen, Anwendbaren. Lizenzausgabe. (German) Zbl 0675.00002
Deutsch-Taschenbücher, 63. Thun etc.: Harri Deutsch. 205 S. SFr. 14.80 (1989).
Reviewer: J.Dieudonné
MSC:  00A99 00A05
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\textit{J. Naas} and \textit{W. Tutschke}, Große Sätze und schöne Beweise der Mathematik: Identität des Schönen, Allgemeinen, Anwendbaren. Lizenzausgabe. Thun etc.: Harri Deutsch (1989; Zbl 0675.00002)

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