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Descriptive set theory over hyperfinite sets

Published online by Cambridge University Press:  12 March 2014

H. Jerome Keisler,
Kenneth Kunen,
Arnold Miller and
Steven Leth
H. Jerome Keisler
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Kenneth Kunen
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Arnold Miller
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Steven Leth*
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
*
Department of Mathematics, University of Northern Colorado, Greeley, Colorado 80639
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Abstract

The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 4 , December 1989, pp. 1167 - 1180
Copyright
Copyright © Association for Symbolic Logic 1989

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References

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