Linked bibliography for the SEP article "The Epsilon Calculus" by Jeremy Avigad and Richard Zach

This is an automatically generated and experimental page

If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

This experiment has been authorized by the editors of the Stanford Encyclopedia of Philosophy. The original article and bibliography can be found here.

Aguilera, J.P., Baaz, M., 2019, ‘Unsound inferences make proofs shorter’. Journal of Symbolic Logic 84: 102–122. (Scholar)
Ackermann, W., 1924, ‘Begründung des ’’tertium non datur’’ mittels der Hilbertschen Theorie der Widerspruchsfreiheit’, Mathematische Annalen, 93: 1–36. (Scholar)
–––, 1937–38, ‘Mengentheoretische Begründung der Logik’, Mathematische Annalen, 115: 1–22. (Scholar)
–––, 1940, ‘Zur Widerspruchsfreiheit der Zahlentheorie’, Mathematische Annalen, 117: 162–194. (Scholar)
Arai, T., 2002, ‘Epsilon substitution method for theories of jump hierarchies’, Archive for Mathematical Logic, 2: 123–153. (Scholar)
–––, 2003, ‘Epsilon substitution method for ID\(_1 (\Pi^{0}_1 \vee \Sigma^{0}_1)\)’, Annals of Pure and Applied Logic, 121: 163–208. (Scholar)
–––, 2006, ‘Epsilon substitution method for \(\Pi^{0}_2\)-FIX. Journal of Symbolic Logic 71: 1155–1188 (Scholar)
Avigad, J., 2002a, ‘Saturated models of universal theories’, Annals of Pure and Applied Logic, 118: 219–234. (Scholar)
–––, 2002b, ‘Update procedures and the 1-consistency of arithmetic’, Mathematical Logic Quarterly, 48: 3–13. (Scholar)
Baaz, M., Leitsch, A., Lolic, A., 2018, ‘A sequent-calculus based formulation of the extended first epsilon theorem’, in: Artemov, S., Nerode, A. (eds.), Logical Foundations of Computer Science, Berlin: Springer, 55–71.
Bell, J. L., 1993a. ‘Hilbert’s epsilon-operator and classical logic’, Journal of Philosophical Logic, 22: 1–18. (Scholar)
–––, 1993b. ‘Hilbert’s epsilon operator in intuitionistic type theories’, Mathematical Logic Quarterly, 39: 323–337. (Scholar)
Bellotti, L., 2016, ‘Von Neumann’s consistency proof’, Review of Symbolic Logic, 9: 429–455. (Scholar)
Bourbaki, N., 1958, Theorie des ensembles, Paris: Hermann. (Scholar)
Buss, S., 1995, ‘On Herbrand’s theorem’, Logic and Computational Complexity (Lecture Notes in Computer Science 960), Berlin: Springer, 195–209. (Scholar)
––– 1998, ‘Introduction to proof theory’, in: Buss (ed.), The Handbook of Proof Theory, Amsterdam: North-Holland, 1–78. (Scholar)
Chierchia, G., 1992. ‘Anaphora and dynamic logic’. Linguistics and Philosophy, 15: 111–183. (Scholar)
Davis, M., and R. Fechter, 1991, ‘A free variable version of the first-order predicate calculus’, Journal of Logic and Computation, 1: 431–451.
DeVidi, D., 1995. ‘Intuitionistic \(\varepsilon\)- and \(\tau\)-calculi’, Mathematical Logic Quarterly 41: 523–546. (Scholar)
Egli, U., von Heusinger, K., 1995, ‘The epsilon operator and E-type pronouns’, in U. Egli et al. (eds.), Lexical Knowledge in the Organization of Language, Amsterdam: Benjamins, 121–141 (Current Issues in Linguistic Theory 114). (Scholar)
Evans, G., 1980, ‘Pronouns’, Linguistic Inquiry, 11: 337–362. (Scholar)
Ewald, W. B. (ed.), 1996, From Kant to Hilbert. A Source Book in the Foundations of Mathematics, Vol. 2, Oxford: Oxford University Press. (Scholar)
Ferrari, P. L., 1987, ‘A note on a proof of Hilbert’s second \(\varepsilon\)-theorem’, Journal of Symbolic Logic, 52: 214–215. (Scholar)
Fine, K., 1985. Reasoning with Arbitrary Objects, Oxford: Blackwell. (Scholar)
Fitting, M., 1975. ‘A modal logic epsilon-calculus’, Notre Dame Journal of Formal Logic, 16: 1–16.
Flannagan, T. B., 1975, ‘On an extension of Hilbert’s second \(\varepsilon\)-theorem’, Journal of Symbolic Logic, 40: 393–397. (Scholar)
Girard, J.-Y., 1982, ‘Herbrand’s theorem and proof theory’, Proceedings of the Herbrand Symposium, Amsterdam: North-Holland, 29-38. (Scholar)
Herbrand, J., 1930, Recherches sur la thèorie de la dèmonstration, Dissertation, University of Paris. English translation in Herbrand 1971, pp. 44–202. (Scholar)
–––, 1971, Logical Writings, W. Goldfarb (ed.), Cambridge, Mass.: Harvard University Press. (Scholar)
Hilbert, D., 1922, ‘Neubegründung der Mathematik: Erste Mitteilung’, Abhandlungen aus dem Seminar der Hamburgischen Universität, 1: 157–177, English translation in Mancosu, 1998, 198–214 and Ewald, 1996, 1115–1134. (Scholar)
–––, 1923, ‘Die logischen Grundlagen der Mathematik’, Mathematische Annalen, 88: 151–165, English translation in Ewald, 1996, 1134–1148. (Scholar)
Hilbert, D., Bernays, P., 1934, Grundlagen der Mathematik, Vol. 1, Berlin: Springer. (Scholar)
–––, 1939, Grundlagen der Mathematik, Vol. 2, Berlin: Springer. (Scholar)
–––, 1970, ‘Grundlagen der Mathematik’, Vol. 2, 2nd, edition, Berlin: Springer, Supplement V. (Scholar)
Hintikka, J., Kulas, J., 1985. Anaphora and Definite Descriptions: Two Applications of Game-Theoretical Semantics, Dordrecht: Reidel. (Scholar)
Kempson, R., Meyer Viol, W., and Gabbay, D., 2001. Dynamic Syntax: The Flow of Language Understanding, Oxford: Blackwell. (Scholar)
Kreisel, G, 1951, ‘On the interpretation of non-finitist proofs – part I’, Journal of Symbolic Logic, 16: 241–267. (Scholar)
Leisenring, A. C., 1969, Mathematical Logic and Hilbert’s Epsilon-Symbol, London: Macdonald. (Scholar)
Luckhardt, H., 1989, ‘Herbrand-Analysen zweier Beweise des Satzes von Roth: Polynomiale Anzahlschranken’, Journal of Symbolic Logic, 54: 234–263. (Scholar)
Maehara, S., 1955, ‘The predicate calculus with \(\varepsilon\)-symbol’, Journal of the Mathematical Society of Japan, 7: 323–344. (Scholar)
–––, 1957, ‘Equality axiom on Hilbert’s \(\varepsilon\)-symbol’, Journal of the Faculty of Science, University of Tokyo, Section 1, 7: 419–435. (Scholar)
Mancosu, P. (ed.), 1998, From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s, Oxford: Oxford University Press. (Scholar)
Meyer Viol, W. P. M., 1995a, Instantial Logic. An Investigation into Reasoning with Instances, Ph.D. thesis, University of Utrecht. ILLC Dissertation Series 1995–11. (Scholar)
–––, 1995b. ‘A proof-theoretic treatment of assignments’, Bulletin of the IGPL, 3: 223–243.
Mints, G., 1994, ‘Gentzen-type systems and Hilbert’s epsilon substitution method. I’, Logic, Methodology and Philosophy of Science, IX (Uppsala, 1991), Amsterdam: North-Holland, 91-122. (Scholar)
–––, 1996, ‘Strong termination for the epsilon substitution method’, Journal of Symbolic Logic, 61: 1193–1205. (Scholar)
–––, 2001, ‘The epsilon substitution method and continuity’, in W. Sieg et al. (eds.), Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman, Lecture Notes in Logic 15, Association for Symbolic Logic. (Scholar)
–––, 2008, ‘Cut Elimination for a simple formulation of epsilon calculus’, Annals of Pure and Applied Logic,152 (1–3): 148–160. (Scholar)
–––, 2013. ‘Epsilon substitution for first- and second-order predicate logic’, Annals of Pure and Applied Logic, 164: 733–739. (Scholar)
–––, 2015. ‘Non-deterministic epsilon substitution method for PA and ID\(_1\)’, in: Kahle, R., Rathjen, M. (Eds.), Gentzen’s Centenary: The Quest for Consistency. Berlin: Springer, pp. 479–500. (Scholar)
Mints, G., Tupailo, S., 1999, ‘Epsilon-substitution method for the ramified language and \(\Delta^{1}_1\)-comprehension rule’, in A. Cantini et al. (eds.), Logic and Foundations of Mathematics (Florence, 1995), Dordrecht: Kluwer, 107–130. (Scholar)
Mints, G., Tupailo, S., Buchholz, W., 1996, ‘Epsilon substitution method for elementary analysis’, Archive for Mathematical Logic, 35: 103–130. (Scholar)
Moser, G., 2006, ‘Ackermann’s substitution method (remixed)’, Annals of Pure and Applied Logic, 142 (1–3): 1–18. (Scholar)
Moser, G. and R. Zach, 2006, ‘The epsilon calculus and Herbrand complexity’, Studia Logica, 82(1): 133–155. (Scholar)
Mostowski, A., 1963. ‘The Hilbert epsilon function in many-valued logics’, Acta Philosophica Fennica, 16: 169–188. (Scholar)
Neale, S., 1990, Descriptions, Cambridge, MA: MIT Press. (Scholar)
Reinhart, T., 1992. ‘Wh-in-situ: An apparent paradox’. In: P. Dekker and M. Stokhof (eds.). Proceedings of the Eighth Amsterdam Colloquium, December 17–20, 1991. ILLC. University of Amsterdam, 483–491. (Scholar)
–––, 1997. ‘Quantifier scope: How labor is divided between QR and choice functions’. Linguistics and Philosophy, 20: 335–397. (Scholar)
Shirai, K., 1971, ‘Intuitionistic predicate calculus with \(\varepsilon\)-symbol’, Annals of the Japan Association for Philosophy of Science 4: 49–67. (Scholar)
Sieg, W., 1991, ‘Herbrand analyses’, Archive for Mathematical Logic, 30: 409–441. (Scholar)
Slater, B. H., 1986, ‘E-type pronouns and \(\varepsilon\)-terms’, Canadian Journal of Philosophy, 16: 27–38.
–––, 1988, ‘Hilbertian reference’, Noûs, 22: 283–97. (Scholar)
–––, 1994, ‘The epsilon calculus’ problematic’, Philosophical Papers, 23: 217–42. (Scholar)
–––, 2000, ‘Quantifier/variable-binding’, Linguistics and Philosophy, 23: 309–21. (Scholar)
Tait, W. W., 1960, ‘The substitution method.’ Journal of Symbolic Logic, 30: 175–192. (Scholar)
–––, 1965, ‘Functionals defined by transfinite recursion,’ Journal of Symbolic Logic, 30: 155–174. (Scholar)
–––, 2010. ‘The substitution method revisited.’ in: S. Feferman and W. Sieg (eds.), Proofs, Categories and Computations: Essays in Honor of Grigori Mints, London: College Publications, pp. 131–14. (Scholar)
von Heusinger, K., 1994, Review of Neale (1990). Linguistics 32: 378–385. (Scholar)
–––, 1997. ‘Definite descriptions and choice functions’. In: S. Akama (ed.). Logic, Language and Computation, Dordrecht: Kluwer, 61–91. (Scholar)
–––, 2000, ‘The Reference of Indefinites’, in von Heusinger and Egli, (2000), 265–284. (Scholar)
–––, 2004, ‘Choice functions and the anaphoric semantics of definite NPs’, Research in Language and Computation, 2: 309–329. (Scholar)
von Heusinger, K., Egli, U., (eds.), 2000. Reference and Anaphoric Relations, Dordrecht: Kluwer. (Scholar)
–––, 2000a. ‘Introduction: Reference and the Semantics of Anaphora’, in von Heusinger and Egli (2000), 1–13. (Scholar)
von Heusinger, K., Kempson, R., (eds.), 2004. Choice Functions in Semantics, Special Issue of Research on Language and Computation 2(3). (Scholar)
von Neumann, J., 1927, ‘Zur Hilbertschen Beweistheorie’, Mathematische Zeitschrift, 26: 1–46. (Scholar)
Wang, H., 1963, A Survey of Mathematical Logic, Peking: Science Press. (Scholar)
Winter, Y., 1997. ‘Choice functions and the scopal semantics of indefinites’. Linguistics and Philosophy, 20: 399–467. (Scholar)
Yasuhara, M., 1982, ‘Cut elimination in \(\varepsilon\)-calculi’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 28: 311–316. (Scholar)
Zach, R., 2003, ‘The practice of finitism. Epsilon calculus and consistency proofs in Hilbert’s Program’, Synthese, 137: 211–259. (Scholar)
–––, 2004. ‘Hilbert’s “Verunglückter Beweis”, the first epsilon theorem, and consistency proofs’. History and Philosophy of Logic, 25, 79–94. (Scholar)
–––, 2017. ‘Semantics and proof theory of the epsilon calculus’, in: Ghosh, S., Prasad, S. (Eds.), Logic and Its Applications. ICLA 2017, LNCS. Springer, Berlin, Heidelberg, pp. 27–47. (Scholar)

Generated Sun Jun 4 11:41:50 2023

Applied ethics	Epistemology	History of Western Philosophy	Meta-ethics	Metaphysics	Normative ethics
Philosophy of biology	Philosophy of language	Philosophy of mind	Philosophy of religion	Science Logic and Mathematics	More ...