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Decision procedures for elementary sublanguages of set theory IX. Unsolvability of the decision problem for a restricted subclass of the Δ 0 ‐formulas in set theory

1988; Wiley; Volume: 41; Issue: 2 Linguagem: Inglês

10.1002/cpa.3160410206

1097-0312

Franco Parlamento, Alberto Policriti,

Rough Sets and Fuzzy Logic

Communications on Pure and Applied MathematicsVolume 41, Issue 2 p. 221-251 Article Decision procedures for elementary sublanguages of set theory IX. Unsolvability of the decision problem for a restricted subclass of the Δ0-formulas in set theory Franco Parlamento, Franco Parlamento University of TorinoSearch for more papers by this authorAlberto Policriti, Alberto Policriti Courant InstituteSearch for more papers by this author Franco Parlamento, Franco Parlamento University of TorinoSearch for more papers by this authorAlberto Policriti, Alberto Policriti Courant InstituteSearch for more papers by this author First published: March 1988 https://doi.org/10.1002/cpa.3160410206Citations: 23AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Barwise, J., Admissible Sets and Structures, Springer Verlag, New York, 1975. 2 Breban, M., and Ferro, A., Decision procedures for elementary sub-languages of set theory. III. Restricted classes of formulas involving the power set operator and the general set operator, Advances in Appl. Math. (to appear). 3 Breban, M., Ferro, A., Omodeo, E., and Schwartz, J. T., Decision procedures for elementary sublanguages of set theory. II. Formulas involving restricted quantifiers together with ordinal, integer, map and domain notions, Comm. Pure Appl. Math. 34, 1981, pp. 177–196. 4 Cantone, D., Ferro, A., Micale, B., and Sorace, G., Decision procedures for elementary sublanguages of set theory. IV. Formulae involving a rank operator or one occurrence of ∑(x) = {{y}/y ∑x}, Comm. Pure Appl. Math., 40, 1987, pp. 37–77. 5 Cantone, D., Ferro, A., and Schwartz, J. T., Decision procedures for elementary sublanguages of set theory. V. Multilevel syllogistic extended by the general union operator, Jour. Comp. Sys. Sci. (to appear). 6 Cantone, D., Ferro, A., and Schwartz, J. T., Decision procedures for elementary sublanguages of set theory. VI. Multilevel syllogistic extended by the powerset operator, Comm. Pure Appl. Math. 38, 1985, pp. 549–571. 7 Collins, G. E., and Halpern, J. D., On the interpretability of arithmetic in set theory, Notre Dame Jour. Formal Logic, Vol. XI, No. 4, 1970, 477–483. 8 Ferro, A., Omodeo, E. G., and Schwartz, J. T., Decision procedures for elementary sublanguages of set theory. I. Multilevel syllogistic and some extension, Comm. Pure Appl. Math. 33, 1980, pp. 599–608. 9 Gandy, R. O., Primitive recursive set functions for elementary syntax, Proc. Symp. Pure Math., Vol. 13, Part II, 1974, pp. 63–126. 10 Omodeo, E. G., Decidability and proof procedures for set theory with a choice operator, Ph.D. thesis, New York Univ. 1984,. 11 Parlamento, F., Introduzione alla Metamatematica della Teoria degli Insiemi. Paret Prima. La Matematica Senza Infinito e i Teoremi di Incompletezza, Quaderni di Matematica dell'Universita di Torino, n. 95, 1984. 12 Rogers, M., Theory of Recursive Functions and Effective Computability, McGraw-Hill, 1967. 13 Smullyan, R. M., Theory of Formal Systems, Annals of Mathematics Studies n. 47, Princeton Univ. Press, 1961. 14 Tarski, A., Mostowski, A., and Robinson, R. M., Undecidable Theories, North-Holland, 1953. 15 Tarski, A., and Szmielew, W., Mutual interpretability of some essentially undecidable theories, Proc. Intl. Cong. of Mathematicians (Cambridge 1950,), Vol. 1, p. 734. 16 Bernays, P., A system of axiomatic set theory, Part I, JSL, Vol. 2, 1937. Citing Literature Volume41, Issue2March 1988Pages 221-251 ReferencesRelatedInformation