## Notre Dame Journal of Formal Logic

### Set Mappings on $4$-Tuples

#### Abstract

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.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 59, Number 3 (2018), 405-416.

Dates
Accepted: 21 March 2016
First available in Project Euclid: 26 June 2018

https://projecteuclid.org/euclid.ndjfl/1529978582

Digital Object Identifier
doi:10.1215/00294527-2018-0002

Mathematical Reviews number (MathSciNet)
MR3832089

Zentralblatt MATH identifier
06939328

#### Citation

Mohsenipour, Shahram; Shelah, Saharon. Set Mappings on $4$ -Tuples. Notre Dame J. Formal Logic 59 (2018), no. 3, 405--416. doi:10.1215/00294527-2018-0002. https://projecteuclid.org/euclid.ndjfl/1529978582

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