Defining additive subgroups of the reals from convex subsets

Author:
Michael A. Tychonievich

Journal:
Proc. Amer. Math. Soc. **137** (2009), 3473-3476

MSC (2000):
Primary 03C64; Secondary 14P10

Published electronically:
May 8, 2009

MathSciNet review:
2515416

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a subgroup of the additive group of real numbers and let be infinite and convex in . We show that is definable in and that is definable if has finite rank. This has a number of consequences for expansions of certain o-minimal structures on the real field by multiplicative groups of complex numbers.

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Additional Information

**Michael A. Tychonievich**

Affiliation:
Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210

Email:
tycho@math.ohio-state.edu

DOI:
https://doi.org/10.1090/S0002-9939-09-09914-6

Received by editor(s):
October 1, 2008

Received by editor(s) in revised form:
December 22, 2008, and February 14, 2009

Published electronically:
May 8, 2009

Communicated by:
Julia Knight

Article copyright:
© Copyright 2009
American Mathematical Society

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