Reasoning about iteration in gödel’s class theory

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2741, Issue , 2003, Pages 228-242

  Belinfante, Johan Gijsbertus Frederik ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPLICATION PROGRAMS; AUTOMATION; THEOREM PROVING; ALGORITHMS; COMPUTER SCIENCE; DIGITAL ARITHMETIC; ITERATIVE METHODS; NUMBER THEORY; PROGRAMMING THEORY;

AUTOMATED REASONING; COMPUTER IMPLEMENTATIONS; NATURAL NUMBER; S-ALGORITHMS; TRANSITIVE CLOSURE;

ITERATIVE METHODS; AUTOMATA THEORY;

AUTOMATED REASONING; CLASS FORMATION; GÖDEL'S CLASS THEORY; ITERATION;

EID: 7044273953     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-45085-6_18     Document Type: Conference Paper

References (26)

1. Andrews, P. B., Bishop, M., Issar, S., Nesmith, D., Pfennig, F. and Xi, H., TPS: A theorem-proving system for classical type theory, Journal of Automated Reasoning, vol. 16 (1996), pp. 321–353
2. Andrews, P. B., Proving theorems automatically and interactively with TPS, Special Session SS S3, Automated Reasoning in Mathematics and Logic, American Mathematical Society Meeting No. 975 in Atlanta, GA., March 9, 2002. Abstract 975-03-86
3. Belinfante, J. G. F., On a modification of Gödel’s algorithm for class formation, Association for Automated Reasoning News Letter, No. 34 (1996) pp. 10–15
4. Belinfante, J. G. F., On Quaife’s development of class theory, Association for Automated Reasoning Newsletter, No. 37 (1997) pp. 5–9
5. Belinfante, J. G. F., Computer proofs in Gödel’s class theory with equational definitions for composite and cross, Journal of Automated Reasoning, vol. 22 (1999) pp. 311–339
6. Belinfante, J. G. F., On computer-assisted proofs in ordinal number theory, Journal of Automated Reasoning, vol. 22 (1999), pp. 341–378
7. Belinfante, J. G. F., Gödel’s Algorithm for Class Formation, in Automated Deduction–CADE-17, edited by D. McAllester, Lecture Notes in Artificial Intelligence, vol. 1831, pp. 132–147, Springer-Verlag, Berlin, 2000. (ISBN 3-540-67664-3)
8. Belinfante, J. G. F., The Unifying Concept of Subvariance, in FTP 2000, Third International Workshop on First-Order Theorem Proving, St. Andrews, Scotland, edited by P. Baumgartner and H. Zhang, pp. 56–67, Fachberichte Informatik, Universität Koblenz-Landau, 2000
9. Belinfante, J. G. F., Computer Proofs about Transitive Closure, in International Joint Conference on Automated Reasoning, IJCAR-2001 Short Papers, pp. 11–20, edited by R. Goré, A. Leitsch and T. Nipkow, Technical Report DII 11/01, Siena, Italy, 19–23 June 2001
10. Belinfante, J. G. F., Discovering Theorems using GOEDEL: A Case Study, in Calculemus-2001, 9th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, 21–22 June 2001, Siena, Italy, edited by Steve Linton and Roberto Sebastiani
11. Belinfante, J. G. F., Automated reasoning about the Zermelo-von Neumann cumulative hierarchy, Special Session SS S3, Automated Reasoning in Mathematics and Logic, American Mathematical Society Meeting No. 975 in Atlanta, GA., March 9, 2002. Abstract 975-03-83
12. Bernays, P., Axiomatic Set Theory, North Holland Publishing Co., Amsterdam. First edition: 1958. Second edition: 1968. Republished in 1991 by Dover Publications, New York
13. Boyer, R., Lusk, E., McCune, W., Overbeek, R., Stickel M. and Wos, L., Set theory in first orderlogic: clauses for Gödel’s axioms, Journal of Automated Reasoning, volume 2 (1986), pages 287–327.
14. Boyer, R. S., and Strother Moore, J., A Computational Logic Handbook, Academic Press, 1988
15. Gödel, K., The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory, Princeton University Press, Princeton, 1940
16. McCune, W. W., Otter 3.0 Reference Manual and Guide, Argonne National Laboratory Report ANL–94/6, Argonne National Laboratory, Argonne, IL, January 1994
17. McCune, W., Solution of the Robbins problem, Journal of Automated Reasoning, vol. 19 (1997), pp. 263–276
18. Paulson, L. C., Set Theory for Verification. II. Induction and Recursion, Journal of Automated Reasoning, vol. 15 (1995), pp. 167–215
19. Quaife, A., Automated Deduction in von Neumann-Bernays-Gödel Set Theory, Journal of Automated Reasoning, vol. 8 (1992), pp. 91–147
20. Quaife, A., Automated Development of Fundamental Mathematical Theories, Ph.D. thesis, Univ. of California at Berkeley, Kluwer Acad. Publishers, Dordrecht, 1992
21. Recio, T., and Vélez, M. P., Automatic Discovery of Theorems in Elementary Geometry, Journal of Automated Reasoning, vol. 23 (1999), pp. 63–82
22. Rubin, J. E., Set Theory for the Mathematician, Holden-Day, San Francisco, 1967
23. Shankar, N., A mechanical proof of the Church-Rosser theorem, Journal of the Association for Computing Machinery vol. 35 (1988), pp. 475–522
24. Wiedijk, F., http://www.cs.kun.nl/˜freek/notes/
25. Wos, L. and Pieper, G. W., A Fascinating Country in the World of Computing: Your Guide to Automated Reasoning, World Scientific, Singapore, 1999
26. Wolfram, S., The MathematicaTM Book, Wolfram Media Inc., Champaign, Illinois, 1996.