Definable sets in Mann pairs

Lou van den Dries, Ayhan Günaydin

Research output: Contribution to journalArticle

Abstract

Consider structures (ω,k,γ) where ω is an algebraically closed field of characteristic zero, k is a subfield, and γ is a subgroup of the multiplicative group of ω. Certain pairs (k,γ) have been singled out as Mann pairs in [4]. We give new examples of such Mann pairs, we axiomatize for each Mann pair (k,γ) the first-order theory of (ω,k,γ) in a cleaner way than in [4], and, as the main result of the article, we characterize the subsets of ωn that are definable in (ω,k,γ).

Original languageEnglish (US)
Pages (from-to)2752-2763
Number of pages12
JournalCommunications in Algebra
Volume39
Issue number8
DOIs
StatePublished - Aug 1 2011

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Subfield
Algebraically closed
Multiplicative
Subgroup
First-order
Subset
Zero

Keywords

  • Definability
  • Mann pairs
  • Model theory

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Definable sets in Mann pairs. / van den Dries, Lou; Günaydin, Ayhan.

In: Communications in Algebra, Vol. 39, No. 8, 01.08.2011, p. 2752-2763.

Research output: Contribution to journalArticle

van den Dries, Lou ; Günaydin, Ayhan. / Definable sets in Mann pairs. In: Communications in Algebra. 2011 ; Vol. 39, No. 8. pp. 2752-2763.
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