Directed sets and cofinal types

Todorčević, Stevo

doi:10.1090/S0002-9947-1985-0792822-9

Directed sets and cofinal types
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Trans. Amer. Math. Soc. 290 (1985), 711-723 Request permission

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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The number of inequivalent directed sets

3

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