Essential incompleteness of arithmetic verified by Coq

Lecture Notes in Computer Science

Volumn 3603, Issue , 2005, Pages 245-260

  O'Connor, Russell ^a,b  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER PROGRAMMING LANGUAGES; FORMAL LOGIC; RECURSIVE FUNCTIONS;

AXIOM SYSTEMS; COQ PROOF ASSISTANTS; FIRST ORDER LOGICS; PEANO ARITHMETIC;

THEOREM PROVING;

EID: 26844433591     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11541868_16     Document Type: Conference Paper

References (15)

1. Stanley N. Burris. Logic for mathematics and computer science: Supplementary text. http://www.math.uwaterloo.ca/~snburris/htdocs/LOGIC/stext. html, 1997.
2. Olga Caprotti and Martijn Oostdijk. Formal and efficient primality proofs by use of computer algebra oracles. J. Symb. Comput., 32(1/2):55-70, 2001.
3. Joëlle Despeyroux and André Hirschowitz. Higher-order abstract syntax with induction in coq. In LPAR '94: Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning, pages 159-173, London, UK, 1994. Springer-Verlag.
4. K. Gödel. Ueber Formal Unentscheidbare sätze der Principia Mathematica und Verwandter Systeme l. Monatshefte für Mathematik und Physik, 38:173-198, 1931.
5. english translation: On Formally Undecidable Propositions of Principia Mathematica and Related Systems I, Oliver & Boyd, London, 1962
6. John Harrison. Formalizing basic first order model theory. In Jim Grundy and Malcolm Newey, editors, Theorem Proving in Higher Order Logics: 11th International Conference, TPHOLs '98, volume 1497 of Lecture Notes in Computer Science, pages 153-170, Canberra, Australia, 1998. Springer-Verlag.
7. John Harrison. The HOL-Light manual, 2000.
8. Claude Marche. Fwd: Question about fixpoint. Coq club mailing list correspondence, http://pauillac.inria.fr/pipermail/coq-club/2005/001641.html, [cited 2005-02-07], February 2005.
9. Conor McBride. Dependently Typed Functional Programs and their Proofs. PhD thesis, University of Edinburgh, 1999. Available from http://www.lfcs. infonnatics.ed.ac.uk/reports/00/ECS-LFCS-00-419/.
10. Russell O'Connor. The Gödel-Rosser 1st incompleteness theorem, http://r6.ca/Goedel20050512.tar.gz, March 2005.
11. Richard E. Hodel. An Introduction to Mathematical Logic. PWS Pub. Co., 1995.
12. N. Shankar. Metamathematics, Machines, and Gödel's Proof. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 1994.
13. J. R. Shoenfield. Mathematical Logic. Addison-Wesley, 1967.
14. Allen Stoughton. Substitution revisited. 59(3):317-325, August 1988.
15. The Coq Development Team. The Coq Proof Assistant Reference Manual - Version V8.0, April 2004. http://coq.inria.fr.