Expansions of subfields of the real field by a discrete set

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Abstract

Let K be a subfield of the real field, D⊆K be a discrete set and f :Dn→K be such that f(Dn) is somewhere dense. Then (K, f) defines ℤ. We present several appli- cations of this result. We show that K expanded by predicates for different cyclic multi- plicative subgroups defines ℤ. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire category theorem.

Original languageEnglish (US)
Pages (from-to)167-175
Number of pages9
JournalFundamenta Mathematicae
Volume215
Issue number2
DOIs
StatePublished - Dec 2 2011

Keywords

  • Defining the set of integers
  • Discrete set
  • Real field

ASJC Scopus subject areas

  • Algebra and Number Theory

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