Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778103 | Annals of Pure and Applied Logic | 2017 | 28 Pages |
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 KatÄtov 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 FÏ ideal is Ramsey, while there is a tall co-analytic Ramsey ideal.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
M. HruÅ¡ák, D. Meza-Alcántara, E. Thümmel, C. Uzcátegui,