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Defining additive subgroups of the reals from convex subsets
Author(s):
Michael
A.
Tychonievich
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3473-3476.
MSC (2000):
Primary 03C64;
Secondary 14P10
Posted:
May 8, 2009
MathSciNet review:
2515416
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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.
References:
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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:
10.1090/S0002-9939-09-09914-6
PII:
S 0002-9939(09)09914-6
Received by editor(s):
October 1, 2008,
Received by editor(s) in revised form:
December 22, 2008, and February 14, 2009
Posted:
May 8, 2009
Communicated by:
Julia Knight
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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