On a ubiquitous cardinal
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 by Stephen H. Hechler PDF
 Proc. Amer. Math. Soc. 52 (1975), 348352 Request permission
Abstract:
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.References

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Additional Information
 © Copyright 1975 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 52 (1975), 348352
 MSC: Primary 54A25; Secondary 02K25, 54D99
 DOI: https://doi.org/10.1090/S00029939197503807057
 MathSciNet review: 0380705