A nonhereditary Borel-cover gamma-set

Details A nonhereditary Borel-cover gamma-set A nonhereditary Borel-cover gamma-set

2003-04-25

arxiv.org/abs/math/0304414v1

Mathematics

Logic

7 pages LaTeX2e

Scientific paper

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.

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