Two consistency results on set mappings

Journal of Symbolic Logic 65 (1):333-338 (2000)

Abstract
It is consistent that there is a set mapping from the four-tuples of ω n into the finite subsets with no free subsets of size t n for some natural number t n . For any $n it is consistent that there is a set mapping from the pairs of ω n into the finite subsets with no infinite free sets. For any $n it is consistent that there is a set mapping from the pairs of ω n into ω n with no uncountable free sets
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DOI 10.2307/2586540
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Free Sets for Set-Mappings Relative to a Family of Sets.Antonio Avilés & Claribet Piña - 2017 - Mathematical Logic Quarterly 63 (6):605-613.

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