Directed sets and cofinal types-Reference-Cited by-同舟云学术

Directed sets and cofinal types

Published:1985 Issue:2 Volume:290 Page:711-723
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Todorčević Stevo

Abstract

We show that 1 , ω , ω 1 , ω × ω 1 1,\omega ,{\omega _1},\omega \times {\omega _1} and [ ω 1 ] > ω {[{\omega _1}]^{ > \omega }} are the only cofinal types of directed sets of size ℵ 1 {\aleph _1} , but that there exist many cofinal types of directed sets of size continuum.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1985-290-02/S0002-9947-1985-0792822-9/S0002-9947-1985-0792822-9.pdf

Reference19 articles.

1. Martin’s axiom and first-countable 𝑆- and 𝐿-spaces;Abraham, U.,1984

2. Applications of the proper forcing axiom;Baumgartner, James E.,1984

3. Moore-Smith convergence in general topology;Birkhoff, Garrett;Ann. of Math. (2),1937

4. Oriented systems;Day, Mahlon M.;Duke Math. J.,1944

5. K. J. Devlin, J. Steprāns and W. S. Watson, The number of inequivalent directed sets, Abstracts Amer. Math. Soc. 3 (1982), 253.

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