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Computability over models of decidable theories

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Abstract

Σ-definability in hereditarily finite superstructures over algebraic systems is studied. We prove the Σ-definability criterion, which is then used as a basis for establishing the reduction theorem for regular theories and for obtaining a characterization of simple theories. The idea of a nonstandard recursion theory is developed using subfields of the field of reals as an example. A partial algebraic description is given for a distributive upper semilattice of mΣ-degrees in hereditarily finite superstructures over models of simple theories.

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Authors
  1. V. G. Puzarenko
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Additional information

Dedicated to the 60th birthday of Academician Yu. L. Ershov

Supported by RFFR grant No. 99-01-00600, and through FP “Integration” project 274.

Translated fromAlgebra i Logika, Vol. 39, No. 2, pp. 170–197, March–April, 2000.

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Puzarenko, V.G. Computability over models of decidable theories. Algebr Logic 39, 98–113 (2000). https://doi.org/10.1007/BF02681664

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  • DOI: https://doi.org/10.1007/BF02681664

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