Journal of the Mathematical Society of Japan

Partition calculus and cardinal invariants

Shimon GARTI and Saharon SHELAH

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We prove that the strong polarized relation $\binom{\theta}{\omega} \rightarrow \binom{\theta}{\omega}^{1,1}_2$, applied simultaneously for every $\theta\in[\aleph_1,2^{\aleph_0}]$, is consistent with ZFC. Consequently, $\binom{inv}{\omega} \rightarrow \binom{inv}{\omega}^{1,1}_2$ is consistent for every cardinal invariant of the continuum. Some results in this direction are generalized to higher cardinals.

Nous prouvons que la relation polarisée forte $\binom{\theta}{\omega} \rightarrow \binom{\theta}{\omega}^{1,1}_2$, appliquée simultanément à chaque cardinal $\theta\in[\aleph_1,2^{\aleph_0}]$, est en accord avec ZFC. Par conséquent, la relation $\binom{inv}{\omega} \rightarrow \binom{inv}{\omega}^{1,1}_2$ est en accord avec ZFC pour chaque caractéristique sur le continu. Nous étudions plusieurs généralisations pour certains cardinaux élevés.

Article information

J. Math. Soc. Japan, Volume 66, Number 2 (2014), 425-434.

First available in Project Euclid: 23 April 2014

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Zentralblatt MATH identifier

Primary: 03E02: Partition relations
Secondary: 03E04: Ordered sets and their cofinalities; pcf theory 03E05: Other combinatorial set theory 03E17: Cardinal characteristics of the continuum 03E35: Consistency and independence results

partition calculus cardinal characteristics


GARTI, Shimon; SHELAH, Saharon. Partition calculus and cardinal invariants. J. Math. Soc. Japan 66 (2014), no. 2, 425--434. doi:10.2969/jmsj/06620425.

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