A nonhereditary Borel-cover gamma-set
逻辑
2007-05-23 v1
摘要
In this paper we prove that if there is a Borel-cover gamma-set of cardinality the continuum, then there is one which is not hereditary. A set of reals X is a Borel-cover gamma-set iff for every countable family of Borel sets which is an omega-cover contains a gamma-cover. This is also denoted S_1(Borel_omega, Borel_gamma). This result partially answers a question of Bartoszynski and Tsaban. Tsaban points out that it also gives an example of set which is both a gamma-set and sigma-set but is not hereditarily gamma, which answers a question of Bukovsky, Reclaw, and Repicky.
引用
@article{arxiv.math/0304414,
title = {A nonhereditary Borel-cover gamma-set},
author = {Arnold W. Miller},
journal= {arXiv preprint arXiv:math/0304414},
year = {2007}
}
备注
7 pages LaTeX2e