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

Author:
Philipp Hieronymi

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2163-2168

MSC (2010):
Primary 03C64; Secondary 14P10

DOI:
https://doi.org/10.1090/S0002-9939-10-10268-8

Published electronically:
February 2, 2010

MathSciNet review:
2596055

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be closed and discrete and be such that is somewhere dense. We show that defines . As an application, we get that for every with , the real field expanded by the two cyclic multiplicative subgroups generated by and defines .

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Additional Information

**Philipp Hieronymi**

Affiliation:
Department of Mathematics & Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada

Address at time of publication:
Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801

Email:
P@hieronymi.de

DOI:
https://doi.org/10.1090/S0002-9939-10-10268-8

Received by editor(s):
July 28, 2009

Received by editor(s) in revised form:
August 20, 2009, September 15, 2009, and October 22, 2009

Published electronically:
February 2, 2010

Communicated by:
Julia Knight

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.