Santos, Paulo Guilherme; Sieg, Wilfried; Kahle, Reinhard A new perspective on completeness and finitist consistency. (English) Zbl 07942593 J. Log. Comput. 34, No. 6, 1179-1198 (2024). MSC: 03-XX 68-XX × Cite Format Result Cite Review PDF Full Text: DOI
Nemoto, Takako; Kentaro, Sato A marriage of Brouwer’s intuitionism and Hilbert’s finitism. I: Arithmetic. (English) Zbl 1510.03023 J. Symb. Log. 87, No. 2, 437-497 (2022). Reviewer: Lukasz Stepien (Kraków) MSC: 03F25 03F35 03F50 03F55 03F60 × Cite Format Result Cite Review PDF Full Text: DOI
Schirn, Matthias Finitist consistency proofs and the impact of Gödel’s incompleteness theorems on Hilbert’s metamathematics. (English) Zbl 1513.03104 J. Appl. Log. - IfCoLog J. Log. Appl. 5, No. 6, 1273-1300 (2018). MSC: 03F40 03F30 03-03 01A60 × Cite Format Result Cite Review PDF
Toffalori, Carlo H for Hilbert. …and M for mathematics. (English) Zbl 1435.03011 Lett. Mat., Int. Ed. 5, No. 2, 119-123 (2017). MSC: 03-03 01A60 × Cite Format Result Cite Review PDF Full Text: DOI
Rinaldi, Davide; Schuster, Peter; Wessel, Daniel Eliminating disjunctions by disjunction elimination. (English) Zbl 1455.03074 Bull. Symb. Log. 23, No. 2, 181-200 (2017). MSC: 03F03 03E25 03F65 × Cite Format Result Cite Review PDF Full Text: DOI
Pohlers, Wolfram Hilbert’s programme and ordinal analysis. (English) Zbl 1433.03132 Probst, Dieter (ed.) et al., Concepts of proof in mathematics, philosophy, and computer science. Based on the Humboldt-Kolleg, Bern, Switzerland, September 9–13, 2013. Ontos Mathematical Logic 6. Berlin: De Gruyter. 291-322 (2016). MSC: 03F03 03F05 03A05 03F15 03F35 × Cite Format Result Cite Review PDF Full Text: DOI
Crosilla, Laura; Schuster, Peter Finite methods in mathematical practice. (English) Zbl 1329.03013 Link, Godehard (ed.), Formalism and beyond. On the nature of mathematical discourse. Berlin: De Gruyter (ISBN 978-1-61451-829-7/hbk; 978-1-61451-847-1/ebook). Logos 23, 351-410 (2014). Reviewer: Victor V. Pambuccian (Phoenix) MSC: 03A05 03F65 01A60 13L05 03-03 × Cite Format Result Cite Review PDF Full Text: DOI
Schuster, Peter M. Induction in algebra: a first case study. (English) Zbl 1277.03065 Log. Methods Comput. Sci. 9, No. 3, Paper No. 20, 19 p. (2013). Reviewer: Johan Georg Granström (Zürich) MSC: 03F65 16Z05 06B10 06F10 03E25 68W30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tapp, Christian On the limit of the finite. The Hilbert programme in the context of formalism and finitism. (An den Grenzen des Endlichen. Das Hilbertprogramm im Kontext von Formalismus und Finitismus.) (German) Zbl 1267.03005 Mathematik im Kontext. Heidelberg: Springer Spektrum (ISBN 978-3-642-29653-6/pbk; 978-3-642-29654-3/ebook). xiii, 376 p. (2013). Reviewer: Elliott Mendelson (Flushing) MSC: 03-03 00A30 01A60 03-02 03A05 03F03 03F40 × Cite Format Result Cite Review PDF Full Text: DOI
Schuster, Peter Induction in algebra: a first case study. (English) Zbl 1364.03086 Proceedings of the 2012 27th annual ACM/IEEE symposium on logic in computer science, LICS 2012, Dubrovnik, Croatia, June 25–28, 2012. Los Alamitos, CA: IEEE Computer Society (ISBN 978-0-7695-4769-5). 581-585 (2012). MSC: 03F65 16Z05 06B10 06F10 03E25 68W30 × Cite Format Result Cite Review PDF Full Text: DOI
Burgess, John P. On the outside looking in: a caution about conservativeness. (English) Zbl 1241.03003 Feferman, Solomon (ed.) et al., Kurt Gödel. Essays for his centennial. Cambridge: Cambridge University Press; Ithaca, NY: Association for Symbolic Logic (ASL) (ISBN 978-0-521-11514-8/hbk). Lecture Notes in Logic 33, 128-141 (2010). Reviewer: Liesbeth De Mol (Gent) MSC: 03A05 03-03 01A60 03B30 × Cite Format Result Cite Review PDF
Sernadas, Amílcar; Sernadas, Cristina Foundations of logic and theory of computation. (English) Zbl 1191.03001 Texts in Computing 10. London: King’s College Publications (ISBN 978-1-904987-88-8). xii, 337 p. (2008). MSC: 03-01 × Cite Format Result Cite Review PDF
Cleland, Carol E. The Church-Turing thesis. A last vestige of a failed mathematical program. (English) Zbl 1105.03007 Olszewski, Adam (ed.) et al., Church’s thesis after 70 years. Frankfurt: Ontos Verlag (ISBN 3-938793-09-0/hbk). Ontos Mathematical Logic 1, 119-146 (2006). Reviewer: Cristian S. Calude (Auckland) MSC: 03A05 03B25 03D10 03D20 03-03 × Cite Format Result Cite Review PDF
Takeuti, Gaisi Incompleteness theorem and its frontier. (English) Zbl 1084.03047 Baaz, Matthias (ed.) et al., Logic colloquium ’01. Proceedings of the annual European summer meeting of the Association for Symbolic Logic (ASL), Vienna, Austria, August 6–11, 2001. Wellesley, MA: A K Peters; Urbana, IL: Association for Symbolic Logic (ISBN 1-56881-247-7/hbk; 1-56881-248-5/pbk). Lecture Notes in Logic 20, 434-439 (2005). Reviewer: Volker Halbach (Oxford) MSC: 03F30 03F40 03D15 03-03 01A60 × Cite Format Result Cite Review PDF
Franco de Oliveira, Augusto J. Hilbert’s formalism vs. intuitive thought. (Portuguese. English summary) Zbl 1070.03501 Bol. Soc. Port. Mat. 52, 1-25 (2005). MSC: 03-03 01A60 03A05 × Cite Format Result Cite Review PDF
Zach, Richard Hilbert’s ‘Verunglückter Beweis’, the first epsilon theorem, and consistency proofs. (English) Zbl 1069.03002 Hist. Philos. Log. 25, No. 2, 79-94 (2004). Reviewer: Jan Waszkiewicz (Wrocław) MSC: 03-03 01A60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Facchini, Alessandro [Miéville, Denis] “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 × Cite Format Result Cite Review PDF
Takeuti, Gaisi Yasugi, Mariko (ed.); Passell, Nicholas (ed.) Memoirs of a proof theorist. Gödel and other logicians. Transl. from the 1998 revised Japanese edition by Mariko Yasugi and Nicholas Passell. (English) Zbl 1030.01030 River Edge, NJ: World Scientific. xviii, 135 p. (2003). Reviewer: Volker Peckhaus (Paderborn) MSC: 01A70 01A60 01-02 03A05 × Cite Format Result Cite Review PDF
Torres Alcaraz, Carlos Hilbert’s second problem on the compatibility of the axioms of arithmetic. (Spanish) Zbl 1045.03004 Misc. Mat. 29, 73-97 (1999). Reviewer: Elliott Mendelson (Flushing) MSC: 03-03 01A60 03A05 03B30 03F30 × Cite Format Result Cite Review PDF
Kreisel, G. Second thoughts around some of Gödel’s writings: A non-academic option. (English) Zbl 0935.01009 Synthese 114, No. 1, 99-160 (1998). Reviewer: V.Peckhaus (Erlangen) MSC: 01A60 03-03 03A05 × Cite Format Result Cite Review PDF Full Text: DOI
Detlefsen, Michael Philosophy of mathematics in the twentieth century. (English) Zbl 0978.03002 Shanker, Stuart G. (ed.), Routledge history of philosophy. Vol. IX: Philosophy of science, logic and mathematics in the twentieth century. London: Routledge. 50-123 (1996). Reviewer: Roman Murawski (Poznań) MSC: 03-03 00A30 03A05 01A60 × Cite Format Result Cite Review PDF
Feferman, Solomon Kreisel’s “unwinding” program. (English) Zbl 0889.03045 Odifreddi, Piergiorgio (ed.), Kreiseliana: about and around Georg Kreisel. Wellesley, MA: A K Peters. 247-273 (1996). Reviewer: V.Peckhaus (Erlangen) MSC: 03F03 03F65 03A05 × Cite Format Result Cite Review PDF
Torres, Carlos The philosophy and the programme of Hilbert. (English) Zbl 0885.03002 Ramirez, Santiago (ed.) et al., Mexican studies in the history and philosophy of science. Dordrecht: Kluwer Academic Publishers. Boston Stud. Philos. Sci. 172, 151-172 (1995). MSC: 03-03 03A05 00A30 01A60 × Cite Format Result Cite Review PDF
Gauthier, Yvon Hilbert and the internal logic of mathematics. (English) Zbl 0814.03001 Synthese 101, No. 1, 1-14 (1994). MSC: 03-03 01A60 01A55 × Cite Format Result Cite Review PDF
Majer, Ulrich Different forms of finitism. (English) Zbl 0838.03003 Czermak, Johannes (ed.), Philosophy of mathematics. Proceedings of the 15th international Wittgenstein-Symposium, 16-23 August 1992, Kirchberg am Wechsel, Austria. Part I. Wien: Hölder-Pichler-Tempsky. Schriftenreihe der Wittgenstein-Gesellschaft. 20/I, 185-194 (1993). Reviewer: V.Peckhaus (Erlangen) MSC: 03A05 00A30 01A60 03-03 × Cite Format Result Cite Review PDF
Smoryński, C. Hilbert’s programme. (English) Zbl 0665.03001 CWI Q. 1, No. 4, 3-59 (1988). Reviewer: R.Murawski MSC: 03-03 00A30 01A60 × Cite Format Result Cite Review PDF