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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On $ Q$ sets


Authors: William G. Fleissner and Arnold W. Miller
Journal: Proc. Amer. Math. Soc. 78 (1980), 280-284
MSC: Primary 03E35; Secondary 54A25, 54A35, 54E30
DOI: https://doi.org/10.1090/S0002-9939-1980-0550513-4
MathSciNet review: 550513
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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_\sigma }$ relative to X. It is known that the 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 then 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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0550513-4
Keywords: Q set, iterated forcing, pathological sets of reals, normal Moore space conjecture
Article copyright: © Copyright 1980 American Mathematical Society