Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Logic
2022-04-19 v2
Abstract
The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of reals of size . In the other direction, it is shown that the existence of both a strongly Luzin set and a coherent Souslin tree is compatible with the existence of a countable partition of pairs of countable ordinals such that no coloring is strong over it. This clarifies the interaction between a gallery of coloring assertions going back to Luzin and Sierpinski a hundred years ago.
Keywords
Cite
@article{arxiv.2104.09148,
title = {Ramsey theory over partitions III: Strongly Luzin sets and partition relations},
author = {Menachem Kojman and Assaf Rinot and Juris Steprans},
journal= {arXiv preprint arXiv:2104.09148},
year = {2022}
}
Comments
To appear in Proceedings of the American Mathematical Society