Partition Calculus and Cardinal Invariants

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.

13 pages

References in corpus (4)

• A strong polarized relation
• The ultrafilter number for singular cardinals
• Combinatorial Aspects of the Splitting Number
• Strong polarized relations for the continuum

Cited by in corpus (9)

• Negating the Galvin Property
• Tiltan
• Polarized relations at singulars over successors
• Amenable colorings
• The Polarised Partition Relation for Order Types
• Cardinal characteristics of the continuum and partitions
• On configurations concerning cardinal characteristics at regular cardinals
• Galvin's property at large cardinals and an application to partition calculus
• Superclub, splitting, separating statements