Defining the set of integers in expansions of the real field by a closed discrete set

Philipp Hieronymi

Research output: Contribution to journalArticlepeer-review

Abstract

Let D ⊆ ℝ be closed and discrete and f : Dn → R be such that f (Dn) is somewhere dense. We show that (ℝ, +,-,f) defines ℤ.As an application, we get that for every α, β ∈ ℝ> o with logα (β) ℚ, the real field expanded by the two cyclic multiplicative subgroups generated by α and β defines ℤ.

Original languageEnglish (US)
Pages (from-to)2163-2168
Number of pages6
JournalProceedings of the American Mathematical Society
Volume138
Issue number6
DOIs
StatePublished - Jun 2010

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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