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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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 a ubiquitous cardinal
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by Stephen H. Hechler PDF
Proc. Amer. Math. Soc. 52 (1975), 348-352 Request permission


We consider five combinatorial or topological structures, each with a certain associated minimal cardinal, and we show that these cardinals are always equal even though it is independent of the axioms of set theory as to just what the value of this common cardinal is. The five structures are the set of functions from $N$ (the set of natural numbers) into $N$ under two partial orderings, the rational numbers with respect to closed embeddings into powers of $N$, a certain subset of $\beta N - N$ with respect to clopen decompositions, the irrationals with respect to compact decompositions, and a subclass of the Borel sets with respect to closed decompositions. The proofs presented do not require a knowledge of forcing techniques.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 348-352
  • MSC: Primary 54A25; Secondary 02K25, 54D99
  • DOI:
  • MathSciNet review: 0380705