Topology and its Applications
Volume 17, Issue 2 , March 1984, Pages 145-155
Gamma-sets and other singular sets of real numbers
Fred Galvin
Arnold W. Miller
Abstract
A family of open subsets U of the real line is called omega-cover
of a set X iff every finite subset of X is contained in an element
of U. A set of reals X is a gamma-set iff for every omega-cover U of
X there exists sequence U0,U1,.. from U such that every element of X
is in all but finitely many Un. In this paper we show that assuming
Martin's axiom there is a gamma-set of cardinality the continuum.