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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Prestel, A., Delzell, C.N. (2011). Model Theory of Several Algebraic Theories. In: Mathematical Logic and Model Theory. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-2176-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2176-3_5
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2175-6
Online ISBN: 978-1-4471-2176-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)