In this article, we study set mappings on 4-tuples. We continue a previous work of Komjath and Shelah by getting new finite bounds on the size of free sets in a generic extension. This is obtained by an entirely different forcing construction. Moreover, we prove a ZFC result for set mappings on 4-tuples. Also, as another application of our forcing construction, we give a consistency result for set mappings on triples.
"Set Mappings on -Tuples." Notre Dame J. Formal Logic 59 (3) 405 - 416, 2018. https://doi.org/10.1215/00294527-2018-0002