Journal of Symbolic Logic

Filters, Cohen Sets and Consistent Extensions of the Erdos-Dushnik-Miller Theorem

Saharon Shelah and Lee J. Stanley

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Abstract

We present two different types of models where, for certain singular cardinals $\lambda$ of uncountable cofinality, $\lambda \rightarrow (\lambda,\omega + 1)^2$, although $\lambda$ is not a strong limit cardinal. We announce, here, and will present in a subsequent paper, [7], that, for example, consistently, $\aleph_{\omega_1} \nrightarrow (\aleph_{\omega_1}, \omega + 1)^2$ and consistently, 2$^{\aleph_0} \nrightarrow (2^{\aleph_0},\omega + 1)^2$.

Article information

Source
J. Symbolic Logic, Volume 65, Issue 1 (2000), 259-271.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746019

Mathematical Reviews number (MathSciNet)
MR1782118

Zentralblatt MATH identifier
0946.03058

JSTOR
links.jstor.org

Citation

Shelah, Saharon; Stanley, Lee J. Filters, Cohen Sets and Consistent Extensions of the Erdos-Dushnik-Miller Theorem. J. Symbolic Logic 65 (2000), no. 1, 259--271. https://projecteuclid.org/euclid.jsl/1183746019


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