On $Q$ sets
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- by William G. Fleissner and Arnold W. Miller
- Proc. Amer. Math. Soc. 78 (1980), 280-284
- DOI: https://doi.org/10.1090/S0002-9939-1980-0550513-4
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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.References
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Bibliographic Information
- © Copyright 1980 American Mathematical Society
- 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