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Two consistency results on set mappings

Published online by Cambridge University Press:  12 March 2014

Péter Komjáth
Department of Computer Science, Eötvös University, Budapest, Rákóczi Út 5, 1088, Hungary, E-mail:
Saharon Shelah
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:


It is consistent that there is a set mapping from the four-tuples of ωn into the finite subsets with no free subsets of size tn for some natural number tn. For any n < ω it is consistent that there is a set mapping from the pairs of ωn into the finite subsets with no infinite free sets. For any n < ω it is consistent that there is a set mapping from the pairs of ωn into ωn with no uncountable free sets.

Research Article
Copyright © Association for Symbolic Logic 2000

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