Filters, Cohen sets and consistent extensions of the Erdos-Dushnik-Miller theorem

Saharon Shelah; Lee J. Stanley

doi:10.2307/2586535

Filters, Cohen sets and consistent extensions of the Erdos-Dushnik-Miller theorem

Saharon Shelah^*
, Lee J. Stanley

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We present two different types of models where, for certain singular cardinals λ of uncountable cofinality. λ → (λ, ω + 1)², although λ is not a strong limit cardinal. We announce, here, and will present in a subsequent paper, [7], that, for example, consistently, א_ω1, (rightwards arrow with stroke) (א_ω1. ω + 1)³ and consistently. 2^א0 (rightwards arrow with stroke) (2^א0. ω + 1)².

Original language	English
Pages (from-to)	259-271
Number of pages	13
Journal	Journal of Symbolic Logic
Volume	65
Issue number	1
DOIs	https://doi.org/10.2307/2586535
State	Published - Mar 2000

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title = "Filters, Cohen sets and consistent extensions of the Erdos-Dushnik-Miller theorem",

abstract = "We present two different types of models where, for certain singular cardinals λ of uncountable cofinality. λ → (λ, ω + 1)2, although λ is not a strong limit cardinal. We announce, here, and will present in a subsequent paper, [7], that, for example, consistently, אω1, (rightwards arrow with stroke) (אω1. ω + 1)3 and consistently. 2א0 (rightwards arrow with stroke) (2א0. ω + 1)2.",

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Filters, Cohen sets and consistent extensions of the Erdos-Dushnik-Miller theorem

Abstract

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