Article ID Journal Published Year Pages File Type
5778103 Annals of Pure and Applied Logic 2017 28 Pages PDF
Abstract
We study several combinatorial properties of (mostly definable) ideals on countable sets. In several cases, we identify critical ideals for such properties in the Katětov order. In particular, the ideal R generated by the homogeneous subsets of the random graph is critical for the Ramsey property. The question as to whether there is a tall definable Ramsey ideal is raised and studied. It is shown that no tall Fσ ideal is Ramsey, while there is a tall co-analytic Ramsey ideal.
Related Topics
Physical Sciences and Engineering Mathematics Logic
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