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Complexity of the decidability of the unquantified set theory with a rank operator

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Georgian Mathematical Journal

Abstract

The unquantified set theory MLSR containing the symbols ∪, ∖, ≠, ∈,R (R(x) is interpreted as a rank ofx) is considered. It is proved that there exists an algorithm which for any formulaQ of the MLSR theory decides whetherQ is true or not using the spacec|Q|3 (|Q| is the length ofQ).

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References

  1. D. Cantone et al., Decision procedures for elementary sublanguages of set theory IV.Comm. Pure and Appl. Math. 40(1987), 37–77.

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  2. A. Kuzichev, Venn diagram. (Russian)Nauka, Moscow, 1968.

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Author notes

  1. M. Tetruashvili

    Present address: I. Vekua Institute of Applied Mathematics of Tbilisi State University, 2, University St., 380043, Tbilisi, Republic of Georgia

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    1. M. Tetruashvili
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    Tetruashvili, M. Complexity of the decidability of the unquantified set theory with a rank operator. Georgian Mathematical Journal 1, 561–565 (1994). https://doi.org/10.1007/BF02317684

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    • DOI: https://doi.org/10.1007/BF02317684

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