Avoiding the projective hierarchy in expansions of the real field by sequences

Author:
Chris Miller

Journal:
Proc. Amer. Math. Soc. **134** (2006), 1483-1493

MSC (2000):
Primary 03C64; Secondary 26A12

DOI:
https://doi.org/10.1090/S0002-9939-05-08112-8

Published electronically:
October 5, 2005

MathSciNet review:
2199196

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Abstract: Some necessary conditions are given on infinitely oscillating real functions and infinite discrete sets of real numbers so that first-order expansions of the field of real numbers by such functions or sets do not define . In particular, let be such that , as for some , is o-minimal, and the expansion of by the set does not define . Then there exist and such that as .

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Additional Information

**Chris Miller**

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

Email:
miller@math.ohio-state.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-08112-8

Received by editor(s):
February 4, 2004

Received by editor(s) in revised form:
November 17, 2004

Published electronically:
October 5, 2005

Additional Notes:
This research was partially supported by NSF Grant No. DMS-9988855.

Communicated by:
Carl G. Jockusch, Jr.

Article copyright:
© Copyright 2005
American Mathematical Society

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