Logical schemes for first order theories

  • Rostislav E. Yavorsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1234)


The logic \(\mathcal{L}\)(T) of an arbitrary first order theory T is the set of predicate formulas provable in T under every interpretation into the language of T. We prove that if T is an arithmetically correct theory in the language of arithmetic, or T is the theory of fields, the theory of rings, or an inessential extension of the theory of groups, then \(\mathcal{L}\)(T) coincides with the predicate calculus PC. We also study inclusion relations and decidability for the logics of Presburger's arithmetic of addition, Skolem's arithmetic of multiplication and other decidable theories.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Rostislav E. Yavorsky
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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