Free sets for set-mappings relative to a family of sets

摘要

Given a family F of subsets of {1, . . . ,m}, we try to compute the least natural number n such that for every function S : [?_n ]~(<ω) -→ [?_n ]~(<ω) there exists a bijection u : {1, . . . ,m} -→Y ? ?_n such that S(u(A)) ∩ Y ? u(A) for all A ∈ F.