Journal of Symbolic Logic

Multiplicative valued difference fields

Koushik Pal

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

First available in Project Euclid: 4 April 2012

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

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