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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Equivalence of families of functions on the natural numbers


Author: Claude Laflamme
Journal: Trans. Amer. Math. Soc. 330 (1992), 307-319
MSC: Primary 03E35; Secondary 04A20
DOI: https://doi.org/10.1090/S0002-9947-1992-1028761-1
MathSciNet review: 1028761
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Abstract: We present some consequences of the inequality $ \mathfrak{u} < \mathfrak{g}$ among cardinal invariants of the continuum, which has previously been shown to be consistent relative to ZFC. We are interested in its effect on two orderings of families of functions on the natural numbers; in particular we show that, under $ \mathfrak{u} < \mathfrak{g}$, there are exactly five equivalence classes for both orderings (excluding the families bounded by a fixed constant function). This implies, under the same hypothesis, the existence of exactly four classes of rarefaction of measure zero sets.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1028761-1
Article copyright: © Copyright 1992 American Mathematical Society