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arXiv:math/0305036 [math.LO]AbstractReferencesReviewsResources

On relatively analytic and Borel subsets

Arnold W. Miller

Published 2003-05-01Version 1

Define z to be the smallest cardinality of a function f:X->Y with X and Y sets of reals such that there is no Borel function g extending f. In this paper we prove that it is relatively consistent with ZFC to have b<z where b is, as usual, smallest cardinality of an unbounded family in w^w. This answers a question raised by Zapletal. We also show that it is relatively consistent with ZFC that there exists a set of reals X such that the Borel order of X is bounded but there exists a relatively analytic subset of X which is not relatively coanalytic. This answers a question of Mauldin.

Comments: LaTeX2e 10 pages available at http://www.math.wisc.edu/~miller/res/index.html
Categories: math.LO
Subjects: 03E35, 03E17, 03E15
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