Partition Calculus and Cardinal Invariants

Details Partition Calculus and Cardinal Invariants Partition Calculus and Cardinal Invariants

2011-12-25

arxiv.org/abs/1112.5772v1

Mathematics

Logic

12 pages

Scientific paper

We prove that the strong polarized relation of $\theta$ above $\omega$
applied simultaneously for every cardinal in the inetrval $[\aleph_1,\aleph]$
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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