On strongly summable ultrafilters and union ultrafilters-Reference-Cited by-同舟云学术

On strongly summable ultrafilters and union ultrafilters

Published:1987 Issue:1 Volume:304 Page:83-97
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Blass Andreas,Hindman Neil

Abstract

We prove that union ultrafilters are essentially the same as strongly summable ultrafilters but ordered-union ultrafilters are not. We also prove that the existence of ultrafilters of these sorts implies the existence of P P -points and therefore cannot be established in ZFC.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1987-304-01/S0002-9947-1987-0906807-4/S0002-9947-1987-0906807-4.pdf

Reference12 articles.

1. A short proof of Hindman’s theorem;Baumgartner, James E.;J. Combinatorial Theory Ser. A,1974

2. On the combinatorial principle 𝑃(𝔠);Bell, Murray G.;Fund. Math.,1981

3. Ultrafilters related to Hindman’s finite-unions theorem and its extensions;Blass, Andreas,1987

4. Ultrafilters: some old and some new results;Comfort, W. W.;Bull. Amer. Math. Soc.,1977

5. Ramsey’s theorem for 𝑛-parameter sets;Graham, R. L.;Trans. Amer. Math. Soc.,1971

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