Expansions of subfields of the real field by a discrete set

Philipp Hieronymi

doi:10.4064/fm215-2-4

Expansions of subfields of the real field by a discrete set

Philipp Hieronymi

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	167-175
Number of pages	9
Journal	Fundamenta Mathematicae
Volume	215
Issue number	2
DOIs	https://doi.org/10.4064/fm215-2-4
State	Published - 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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10.4064/fm215-2-4

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Expansions of subfields of the real field by a discrete set

Abstract

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