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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
Corresponding

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

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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.Google 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

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