Journal of Symbolic Logic

Forcing Many Positive Polarized Partition Relations between a Cardinal and Its Powerset

Saharon Shelah and Lee J. Stanley

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Abstract

A fairly quotable special, but still representative, case of our main result is that for 2 $\leq$ n $\leq \omega$, there is a natural number m (n) such that, the following holds. Assume GCH: If $\lambda < \mu$ are regular, there is a cofinality preserving forcing extension in which 2$^\lambda = \mu$ and, for all $\sigma < \lambda \leq \kappa < \eta$ such that $\eta^{+m(n)-1)} \leq \mu$, $((\eta^{+m(n)-1)})_\sigma) \rightarrow ((\kappa)_\sigma)_\eta^{(1)n}.$ This generalizes results of [3], Section 1, and the forcing is a "many cardinals" version of the forcing there.

Article information

Source
J. Symbolic Logic, Volume 66, Issue 3 (2001), 1359-1370.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746565

Mathematical Reviews number (MathSciNet)
MR1856747

Zentralblatt MATH identifier
0989.03044

JSTOR
links.jstor.org

Citation

Shelah, Saharon; Stanley, Lee J. Forcing Many Positive Polarized Partition Relations between a Cardinal and Its Powerset. J. Symbolic Logic 66 (2001), no. 3, 1359--1370. https://projecteuclid.org/euclid.jsl/1183746565


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