On relatively analytic and Borel subsets
逻辑
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0305036,
title = {On relatively analytic and Borel subsets},
author = {Arnold W. Miller},
journal= {arXiv preprint arXiv:math/0305036},
year = {2007}
}
备注
LaTeX2e 10 pages available at http://www.math.wisc.edu/~miller/res/index.html