Another proof of a result of Jech and Shelah

Title:

Another proof of a result of Jech and Shelah

Creator:

Komjáth, Péter

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5b741ef6-ef82-4c4c-9931-d961216e268a
uuid:5b741ef6-ef82-4c4c-9931-d961216e268a

Subject:

partially ordered set and pcf theory

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Shelah's pcf theory describes a certain structure which must exist if $\aleph _{\omega }$ is strong limit and $2^{\aleph _\omega }>\aleph _{\omega _1}$ holds. Jech and Shelah proved the surprising result that this structure exists in ZFC. They first give a forcing extension in which the structure exists then argue that by some absoluteness results it must exist anyway. We reformulate the statement to the existence of a certain partially ordered set, and then we show by a straightforward, elementary (i.e., non-metamathematical) argument that such partially ordered sets exist.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

577-582

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:3

Harvested from:

CDK

Metadata only:

false