Journal of Symbolic Logic

Multiplicative valued difference fields

Koushik Pal

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
J. Symbolic Logic, Volume 77, Issue 2 (2012), 545-579.

Dates
First available in Project Euclid: 4 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1333566637

Digital Object Identifier
doi:10.2178/jsl/1333566637

Mathematical Reviews number (MathSciNet)
MR2963021

Zentralblatt MATH identifier
1245.03056

Citation

Pal, Koushik. Multiplicative valued difference fields. J. Symbolic Logic 77 (2012), no. 2, 545--579. doi:10.2178/jsl/1333566637. https://projecteuclid.org/euclid.jsl/1333566637


Export citation