Hostname: page-component-5d59c44645-jb2ch Total loading time: 0 Render date: 2024-02-22T05:49:40.774Z Has data issue: false hasContentIssue false

Two consistency results on set mappings

Published online by Cambridge University Press:  12 March 2014

Péter Komjáth
Affiliation:
Department of Computer Science, Eötvös University, Budapest, Rákóczi Út 5, 1088, Hungary, E-mail: kope@cs.elte.hu
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il

Abstract

It is consistent that there is a set mapping from the four-tuples of ωn into the finite subsets with no free subsets of size tn for some natural number tn. For any n < ω it is consistent that there is a set mapping from the pairs of ωn into the finite subsets with no infinite free sets. For any n < ω it is consistent that there is a set mapping from the pairs of ωn into ωn with no uncountable free sets.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Erdős, P., Some remarks on set theory, Proceedings of the American Mathematical Society, vol. 1 (1950), pp. 127141.CrossRefGoogle Scholar
[2]Erdős, P. and Hajnal, A., On the structure of set mappings, Acta Mathematica Academiae Scientifica Hungarica, vol. 9 (1958), pp. 111131.CrossRefGoogle Scholar
[3]Erdös, P., Hajnal, A., Máté, A., and Rado, R., Combinatorial set theory: Partition relations for cardinals, North-Holland, Akadémiai Kiadö, 1984.Google Scholar
[4]Grünwald, G., Egy halmazelméleti tételről, Mathematikai És Fizikai Lapok, vol. 44 (1937), pp. 5153.Google Scholar
[5]Hajnal, A., Proof of a conjecture of S. Ruziewicz, Fundamenta Mathematicae, vol. 50 (1961), pp. 123128.CrossRefGoogle Scholar
[6]Hajnal, A. and Máté, A., Set mappings, partitions, and chromatic numbers, Logic Colloquium '73, Bristol, North-Holland, 1975, pp. 347379.Google Scholar
[7]KomjÁth, P., A set mapping with no infinite free subsets, this Journal, vol. 56 (1991), pp. 304306.Google Scholar
[8]Kuratowski, K., Sur une charactérization des alephs, Fundamenta Mathematicae, vol. 38 (1951), pp. 1417.CrossRefGoogle Scholar
[9]Piccard, S., Sur un problème de M. Ruziewicz de la thÉorie des relations, Fundamenta Mathematicae, vol. 29 (1937), pp. 59.CrossRefGoogle Scholar
[10]Ruziewicz, S., Une généralisation d'un théorème de M. Sierpiński, Publications Mathématiques de l'Université de Belgrade, vol. 5 (1936), pp. 2327.Google Scholar