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Israel Journal of Mathematics

, Volume 2, Issue 1, pp 55–70 | Cite as

On the decision problem for theories of finite models

  • Verena Huber Dyson
Article

Abstract

An infinite extension of the elementary theory of Abelian groups is constructed, which is proved to be decidable, while the elementary theory of its finite models is shown to be undecidable. Tarski’s proof of undecidability for the elementary theory of Abelian cancellation semigroups is presented in detail. Szmielew’s proof of the decidability of the elementary theory of Abelian groups is used to prove the decidability of the elementary theory of finite Abelian groups, and an axiom system for this theory is exhibited. It follows that the elementary theory of Abelian cancellation semigroups, while undecidable, has a decidable theory of finite models.

Keywords

Abelian Group Decision Problem Decidable Theory Elementary Theory Finite Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1964

Authors and Affiliations

  • Verena Huber Dyson
    • 1
  1. 1.Adelphi CollegeGarden City, Long Island

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