Set mappings on 4-tuples
Shahram Mohsenipour, Saharon Shelah
TL;DR
This paper advances the understanding of set mappings on 4-tuples by providing new bounds, a ZFC result, and a consistency result for triples, using novel forcing techniques.
Contribution
It introduces a new forcing construction to improve bounds on free sets and proves a ZFC result for 4-tuples, also extending to triples.
Findings
New finite bounds on free sets in generic extensions
A ZFC theorem for set mappings on 4-tuples
A consistency result for set mappings on triples
Abstract
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.
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