@techreport{eb9430e777284b51a735177be271d19a,

title = "Sierpinski's onto mapping and partitions",

abstract = " In his 1987 paper, Todorcevic remarks that Sierpinski's onto mapping principle (1932) and the Erdos-Hajnal-Milner negative Ramsey relation (1966) are equivalent to each other, and follow from the existence of a Luzin set. Recently, Guzman and Miller showed that these two principles are also equivalent to the existence of a nonmeager set of reals of cardinality $\aleph_1$. We expand this circle of equivalences and show that these propositions are equivalent also to the high-dimensional version of the Erdos-Hajnal-Milner negative Ramsey relation, thereby improving a CH theorem of Galvin (1980). Then we consider the validity of these relations in the context of strong colorings over partitions and prove the consistency of a positive Ramsey relation, as follows: It is consistent with the existence of both a Luzin set and of a Souslin tree that for some countable partition p, all colorings are p-special. ",

keywords = "math.LO, Primary 03E02, Secondary 03E35, 03E17",

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

year = "2021",

language = "???core.languages.en_GB???",

series = "Arxiv preprint",

type = "WorkingPaper",

}