Set mappings and polarized partition relations
نویسندگان
چکیده
A set mapping on a set 5 is a function f from S into the set of subsets of 5 such that u+f(ti) (YES); AcS is called a free set (for the setmapping)if yqf(u> forall x,yeA, i.e. Anf(A)=c#, Itwasanold conjecture of Ruziewicz cl] that, if IS] = rn’ H, , and if IfcY)I< h (reS), where n is a fixed cardinal less than m, then there is a free set of cardinal m. D. LazLr [2] proved this in the case when m is a regular cardinal and Sophie Piccard [3] proved the conjecture for those cardinals m which are the sums of %I smaller cardinals. Erd& [4] gave a solution of the complete conjecture using the generalized continuum hypothesis, and finally Hajnal [S] proved the result without this hypothesis.
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