Decision procedures for elementary sublanguages of set theory

Journal of Automated Reasoning - Tập 6 - Trang 189-201 - 1990
D. Cantone1,2, V. Cutello1,2
1Department of Computer Science Courant Institute of Mathematical Sciences, New York University, USA
2Department of Mathematics, University of Catania, Italy

Tóm tắt

In this paper we prove the decidability of the class of unquantified formulae of set theory involving the operators ϕ, ∪, ∩, \, {·}, pred < and the predicates =, ∈, $$ \subseteq $$ , Finite, where pred <(s) denotes the collection of all sets having rank strictly less than the rank of s. This work generalizes and combines earlier results published in the same series of papers.

Tài liệu tham khảo

Cantone, D., ‘Decision procedures for elementary sublanguages of set theory. X. Multilevel syllogistic extended by the singleton and powerset operators’, J. Symb. Comp. — Special issue (to appear). New Trends in Automated Mathematical Reasoning-Proceedings. Cantone, D., Cutello, V. and Ferro, A., ‘Decision procedures for elementary sublanguages of set theory. XIV. Three languages involving rank related constructs’, in Int. Symp. on Symbolic and Algebraic Computation (to appear). Cantone, D., Ferro, A., Micale, B. and Sorace, G., ‘y∈x}’, Comm. Pure App. Math. 40, 37–77 (1987). Cantone, D. and Schwartz, J. T., ‘Decision procedures for elementary sublanguages of set theory. XI. Multilevel syllogistic extended by some elementary map constructs’, J. Symb. Comp. — Special issue (to appear). New Trends in Automated Mathematical Reasoning-Proceedings. Jech, T. J., Set Theory, Academic Press, New York (1978). Vaught, R. L., Set Theory. An Introduction, Birkhauser, Boston (1985).