Expansions of subfields of the real field by a discrete set

Philipp Hieronymi

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arXiv · 1012.3508

Expansions of subfields of the real field by a discrete set

Philipp Hieronymi

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Abstract

Let K be a subfield of the real field, D be a discrete subset of K and f : D^n -> K be a function such that f(D^n) is somewhere dense. Then (K,f) defines the set of integers. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines the set of integers. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire Category Theorem.

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BibTeX RIS

Philipp Hieronymi. 2010-12-16. Expansions of subfields of the real field by a discrete set. https://arxiv.org/abs/1012.3508

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