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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1106183-9
PII: S 0002-9939(1993)1106183-9
Keywords: (Ratio)comparison ordering of series, distributivity, base matrix, cardinal characteristics of Boolean algebras and of continuum
Article copyright: © Copyright 1993 American Mathematical Society