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## On Q-sets

Fleissner, William G. ; Miller, Arnold W.

Fleissner, William G.

Miller, Arnold W.

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##### Abstract

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.

##### Description

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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1980-02-01

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American Mathematical Society

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##### Keywords

Q set, iterated forcing, pathological sets of reals, normal Moore space conjecture

##### Citation

Fleissner, William G. & Miller, Arnold W. "On Q-sets." Proc. AMS. (1980) 78, 2. 280-284. http://www.dx.doi.org/10.1090/S0002-9939-1980-0550513-4.

##### DOI

10.1090/S0002-9939-1980-0550513-4