Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 77, Issue 2 (2012), 545-579.
Multiplicative valued difference fields
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.
J. Symbolic Logic, Volume 77, Issue 2 (2012), 545-579.
First available in Project Euclid: 4 April 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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