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arXiv · 1112.5772

Partition Calculus and Cardinal Invariants

Shimon Garti·Saharon Shelah
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Abstract

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive relation is consistent for every cardinal invariant on the continuum. We show that similar results hold for a supercompact cardinal, and for a strong limit singular under some assumptions.

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Shimon Garti, Saharon Shelah. 2011-12-25. Partition Calculus and Cardinal Invariants. https://doi.org/10.2969/jmsj%2F06620425

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