  In this paper 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 and
also as another application of our forcing construction we give a consistency
result for set mappings on triples.
