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Nonuniformization results for the projective hierarchy

Published online by Cambridge University Press:  12 March 2014

Steve Jackson  and
R. Daniel Mauldin
Steve Jackson
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas 76203
R. Daniel Mauldin
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas 76203
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Abstract

Let X and Y be uncountable Polish spaces. We show in ZF that there is a coanalytic subset P of X × Y with countable sections which cannot be expressed as the union of countably many partial coanalytic, or even PCA = , graphs. If X = Y = ωω, P may be taken to be . Assuming stronger set theoretic axioms, we identify the least pointclass such that any such coanalytic P can be expressed as the union of countably many graphs in this pointclass. This last result is extended (under suitable hypotheses) to all levels of the projective hierarchy.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 2 , June 1991 , pp. 742 - 748
Copyright
Copyright © Association for Symbolic Logic 1991

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References

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