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Multiplicative valued difference fields

Published online by Cambridge University Press:  12 March 2014

Koushik Pal
Koushik Pal*
Affiliation:
Department of Mathematics, University of California,Berkeley, Berkeley, CA 94720-3840, USA, E-mail: [email protected]
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Abstract

The theory of valued difference fields (K, σ, υ,) depends on how the valuation υ interacts with the automorphism σ. Two special cases have already been worked out - the isometric case, where υ(σ(x)) = υ(x) for all x Є K, has been worked out by Luc Belair, Angus Macintyre and Thomas Scanlon; and the contractive case, where υ(σ(x)) > nυ(x) for all x Є K× with υ(x) > 0 and n Є ℕ, has been worked out by Salih Azgin. In this paper we deal with a more general version, the multiplicative case, where υ(σ(x)) = ρ · υ(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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 545 - 579
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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