Ramsey theory over partitions III: Strongly Luzin sets and partition relations

Posted on March 30, 2021 by Assaf Rinot in categories: Partition Relations, Publications.

Joint work with Menachem Kojman and Juris Steprāns.

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 $\aleph_1$. 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.

 

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One Response to Ramsey theory over partitions III: Strongly Luzin sets and partition relations

  1. saf says:
    April 16, 2022 at 4:19 pm

    Submitted to Proceedings of the American Mathematical Society, April 2021.
    Accepted, April 2022.

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