Directed sets and cofinal types

Todorčević, Stevo

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

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
DOI: https://doi.org/10.1090/S0002-9947-1985-0792822-9
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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