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Model Theory of Several Algebraic Theories

  • Alexander Prestel
  • Charles N. Delzell
Part of the Universitext book series (UTX)

Abstract

In this chapter we investigate a series of interesting algebraic theories for the properties of completeness, model completeness and quantifier elimination. Not only do we treat the standard examples that have already been frequently treated in the extant literature, but we shall place special value on the theory of valued fields. Since valuation theory does not belong in the standard repertoire of an algebra course, we shall first discuss the necessary concepts and theorems in detail, in Section 4.3. Thereafter we develop special cases (Sections 4.4 and 4.5), and finally the model theory of Henselian valued fields. The goal of this presentation is, among other things, a treatment of a purely number theoretic problem – Artin’s conjecture – in Theorem 4.6.5.

Keywords

Abelian Group Model Theory Axiom System Algebraic Theory Valuation Ring 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Fachbereich Mathematik und StatistikUniversität KonstanzKonstanzGermany
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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