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

 

On strongly discrete subsets of $ \omega\sp \ast$


Author: Mariusz Rabus
Journal: Proc. Amer. Math. Soc. 118 (1993), 1291-1300
MSC: Primary 54D35; Secondary 03E35, 03E50, 54A35
MathSciNet review: 1181172
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Abstract: We prove that it is consistent with Martin's Axiom and $ \neg \mathrm{CH}$ that there is a strongly discrete subspace $ A \subseteq {\omega ^{\ast}}$ of cardinality $ {\aleph _1}$ such that the closure of $ A$ is not homeomorphic with $ \beta {\omega _1}$. We also prove that MA and $ \neg \mathrm{CH}$ imply that there is no convergent strongly discrete subset of $ {\omega ^{\ast}}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1181172-7
PII: S 0002-9939(1993)1181172-7
Keywords: $ \beta \omega $, forcing, Martin's Axiom
Article copyright: © Copyright 1993 American Mathematical Society