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Boolean isomorphism between partial orderings of convergent and divergent series and infinite subsets of $ {\bf N}$

Author: Peter Vojtáš
Journal: Proc. Amer. Math. Soc. 117 (1993), 235-242
MSC: Primary 03E05; Secondary 03E35, 40A05
MathSciNet review: 1106183
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Abstract: We prove that $ \operatorname{RO} (\mathcal{P}(\mathbb{N})/\operatorname{fin} ,\,{ \subseteq ^{\ast}})$ is isomorphic under $ \mathfrak{p} = \operatorname{cf} ({2^{{\aleph _0}}})$ to the Boolean completion of the comparison ordering of the absolutely divergent series (downwards) and under $ {\aleph _1} = \operatorname{cf} ({2^{{\aleph _0}}})$ to the Boolean completion of the ratio comparison ordering of absolutely convergent series (upwards).

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Keywords: (Ratio)comparison ordering of series, distributivity, base matrix, cardinal characteristics of Boolean algebras and of continuum
Article copyright: © Copyright 1993 American Mathematical Society

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