Theories of initial segments of standard models of arithmetics and their complete extensions |
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| Authors: | Micha? Krynicki Jerzy TomasikKonrad Zdanowski |
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| Affiliation: | a Cardinal Stefan Wyszyński University in Warsaw, Polandb Université d’Auvergne, Clermont-Ferrand, Francec Institute of Mathematics, Polish Academy of Science, Warsaw, Poland |
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| Abstract: | We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.We also estimate the complexity of complete extensions of the arithmetic with addition and multiplication. |
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| Keywords: | Finite models Arithmetic Finite arithmetic Presburger arithmetic Decidability |
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