A Q set is an uncountable set X of the real line such that every subset of
X is an F„ relative to X. It is known that die existence of a Q set is independent of
and consistent with the usual axioms of set theory. We show that one cannot prove,
using the usual axioms of set theory: 1. If X is a Q set men any set of reals of
cardinality less than the cardinality of X is a Q set. 2. The union of a Q set and a
countable set is a Q set.
This is the published version, also available here: http://www.dx.doi.org/10.1090/S0002-9939-1980-0550513-4. First published in Proc. AMS. in 1980, published by the American Mathematical Society.
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