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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On $Q$ sets
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by William G. Fleissner and Arnold W. Miller PDF
Proc. Amer. Math. Soc. 78 (1980), 280-284 Request permission

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
  • © 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