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Decision procedures for elementary sublanguages of set theory

XV. Multilevel syllogistic extended by the predicate finite and the operators singleton and pred<

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Abstract

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.

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References

  1. 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.

  2. 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).

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This work has been partially supported by ENI and ENIDATA within the AXL project.

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Cantone, D., Cutello, V. Decision procedures for elementary sublanguages of set theory. J Autom Reasoning 6, 189–201 (1990). https://doi.org/10.1007/BF00245818

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  • DOI: https://doi.org/10.1007/BF00245818

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