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Transactions of the American Mathematical Society

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

 

 

Directed sets and cofinal types


Author: Stevo Todorčević
Journal: Trans. Amer. Math. Soc. 290 (1985), 711-723
MSC: Primary 03E05; Secondary 03E35, 06A10, 18B35, 54A15
MathSciNet review: 792822
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Abstract: We show that $ 1,\omega ,{\omega _1},\omega \times {\omega _1}$ and $ {[{\omega _1}]^{ < \omega }}$ are the only cofinal types of directed sets of size $ {\aleph _1}$, but that there exist many cofinal types of directed sets of size continuum.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0792822-9
Article copyright: © Copyright 1985 American Mathematical Society