Notre Dame Journal of Formal Logic

Set Mappings on 4-Tuples

Shahram Mohsenipour and Saharon Shelah

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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
Received: 19 September 2015
Accepted: 21 March 2016
First available in Project Euclid: 26 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1529978582

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

Mathematical Reviews number (MathSciNet)
MR3832089

Zentralblatt MATH identifier
06939328

Subjects
Primary: 03E05: Other combinatorial set theory 03E35: Consistency and independence results

Keywords
combinatorial set theory set mappings

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


Export citation

References

  • [1] Erdös, P., A. Hajnal, A. Máté, and R. Rado, Combinatorial Set Theory: Partition Relations for Cardinals, vol. 106 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1984.
  • [2] Erdös, P., and R. Rado, “Combinatorial theorems on classifications of subsets of a given set,” Proceedings of the London Mathematical Society, Third Series, vol. 3 (1952), pp. 417–39.
  • [3] Gillibert, P., “Points critiques de couples de varietes d’algebras,” Ph.D. dissertation, University of Caen, Normandy, France, 2008.
  • [4] Gillibert, P., and F. Wehrung, “An infinite combinatorial statement with a poset parameter,” Combinatorica, vol. 31 (2011), pp. 183–200.
  • [5] Graham, R. L., B. L. Rothschild, and J. H. Spencer, Ramsey Theory, second edition, Wiley, New York, 1980.
  • [6] Hajnal, A., “Proof of a conjecture of S. Ruziewicz,” Fundamenta Mathematicae, vol. 50 (1961), pp. 123–28.
  • [7] Hajnal, A., and A. Máté, “Set mappings, partitions, and chromatic numbers,” pp. 347–79 in Logic Colloquium ’73 (Bristol, 1973), vol. 80 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1975.
  • [8] Komjath, P., “A note on set mappings,” in preparation.
  • [9] Komjath, P., and S. Shelah, “Two consistency results on set mappings,” Journal of Symbolic Logic, vol. 65 (2000), pp. 333–38.