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On the Ramsey property for sets of reals

Published online by Cambridge University Press:  12 March 2014

Ilias G. Kastanas
Ilias G. Kastanas*
Affiliation:
California State University, Los Angeles, California 90032
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Abstract

We review some known results about the Ramsey property for partitions of reals, and we present a certain two-person game such that if either player has a winning strategy then a homogeneous set for the partition can be constructed, and conversely. This gives alternative proofs of some of the known results. We then discuss possible uses of the game in obtaining effective versions of Ramsey's theorem and prove a theorem along these lines.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 4 , December 1983 , pp. 1035 - 1045
Copyright
Copyright © Association for Symbolic Logic 1983

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References

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