The real field with an irrational power function and a dense multiplicative subgroup

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Abstract

This paper provides a first example of a model theoretically well-behaved structure consisting of a proper o-minimal expansion of the real field and a dense multiplicative subgroup of finite rank. Under certain Schanuel conditions, a quantifier elimination result will be shown for the real field with an irrational power function xτ and a dense multiplicative subgroup of finite rank whose elements are algebraic over (τ). Moreover, every open set definable in this structure is already definable in the reduct given by just the real field and the irrational power function.

Original languageEnglish (US)
Pages (from-to)153-167
Number of pages15
JournalJournal of the London Mathematical Society
Volume83
Issue number1
DOIs
StatePublished - Feb 2011

ASJC Scopus subject areas

  • Mathematics(all)

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