Theories of initial segments of standard models of arithmetics and their complete extensions

Authors:
Micha Krynicki;Jerzy Tomasik;Konrad Zdanowski
Affiliations:
Cardinal Stefan Wyszyski University in Warsaw, Poland;Université dAuvergne, ClermontFerrand, France;Institute of Mathematics, Polish Academy of Science, Warsaw, Poland
Venue:
Theoretical Computer Science
Year:
2011

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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.