@article{bde18787ba8f45b18c9bbf01c18e357a,

title = "RAMSEY THEORY OVER PARTITIONS III: STRONGLY LUZIN SETS AND PARTITION RELATIONS",

abstract = "The strongest type of coloring of pairs of countable ordinals, gotten by Todor{\v c}evi{\'c} from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of reals of size ℵ1. 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 Sierpi´ nski a hundred years ago.",

author = "Menachem Kojman and Assaf Rinot and Juris Steprāns",

note = "Funding Information: Received by the editors March 31, 2021, and, in revised form, January 4, 2022, and March 30, 2022. 2020 Mathematics Subject Classification. Primary 03E02; Secondary 03E35, 03E17. The first author was partially supported by the Israel Science Foundation (grant agreement 665/20). The second author was partially supported by the Israel Science Foundation (grant agreement 2066/18) and by the European Research Council (grant agreement ERC-2018-StG 802756). The third author was partially supported by NSERC of Canada. 1Two d-tuples (p1,...,pd) and (q1,...,qd) are understood to be disjoint iff {p1,...,pd} ∩ {q1,...,qd}∕ ∅. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society.",

year = "2023",

month = jan,

day = "1",

doi = "10.1090/proc/16106",

language = "English",

volume = "151",

pages = "369--384",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "1",

}