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June 2012 Multiplicative valued difference fields
Koushik Pal
J. Symbolic Logic 77(2): 545-579 (June 2012). DOI: 10.2178/jsl/1333566637

Abstract

The theory of valued difference fields (K,σ,v) depends on how the valuation v interacts with the automorphism σ. Two special cases have already been worked out - the isometric case, where v(σ(x)) = v(x) for all x∈K, has been worked out by Luc Belair, Angus Macintyre and Thomas Scanlon; and the contractive case, where v(σ(x)) > n v(x) for all x∈ K× with v(x) > 0 and n∈ℕ, has been worked out by Salih Azgin. In this paper we deal with a more general version, the multiplicative case, where v(σ(x)) = ρ· v(x), where ρ (> 0) is interpreted as an element of a real-closed field. We give an axiomatization and prove a relative quantifier elimination theorem for this theory.

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Koushik Pal. "Multiplicative valued difference fields." J. Symbolic Logic 77 (2) 545 - 579, June 2012. https://doi.org/10.2178/jsl/1333566637

Information

Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1245.03056
MathSciNet: MR2963021
Digital Object Identifier: 10.2178/jsl/1333566637

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 2 • June 2012
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