Proceedings of the American Mathematical Society

Author(s): Steven C. Leth
Journal: Proc. Amer. Math. Soc. 134 (2006), 1579-1589.
MSC (2000): Primary 11B25, 11B05, 03H05, 03H15
Posted: December 2, 2005
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Abstract: Nonstandard methods are used to obtain results in combinatorial number theory. The main technique is to use the standard part map to translate density properties of subsets of $^{\ast}\mathbb{N}$ into Lebesgue measure properties on

. This allows us to obtain a simple condition on a standard sequence

that guarantees the existence of intervals in arithmetic progression, all of which contain elements of

with various uniform density conditions.

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Steven C. Leth
Affiliation: Department of Mathematical Sciences, University of Northern Colorado, Greeley, Colorado 80639
Email: steven.leth@unco.edu

DOI: 10.1090/S0002-9939-05-08141-4
PII: S 0002-9939(05)08141-4
Keywords: Nonstandard analysis, arithmetic progressions
Received by editor(s): August 31, 2004
Received by editor(s) in revised form: October 14, 2004, November 7, 2004, and January 5, 2005
Posted: December 2, 2005
Additional Notes: The author thanks the referee for identifying several errors in the original version
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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