Title: A nonhereditary Borel-cover gamma-set
Author: A. Miller
Abstract:
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.
http://www.math.wisc.edu/~miller/res/index.html
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Dec 2002 LaTeX2e 6 pages