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Similar but not the same: various versions of ♣ do not coincide

Published online by Cambridge University Press:  12 March 2014

Mirna Džamonja  and
Saharon Shelah
Mirna Džamonja
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK, E-mail: M.Dzamonja@uea.ac.uk
Saharon Shelah
Affiliation:
Mathematics Department, Hebrew University of Jerusalem, 91904 Givat Ram, Israel, E-mail: shelah@sunset.huji.ac.il
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Abstract

We consider various versions of the ♣ principle. This principle is a known consequence of ◊. It is well known that ◊ is not sensitive to minor changes in its definition, e.g., changing the guessing requirement form “guessing exactly” to “guessing modulo a finite set”. We show however, that this is not true for ♣. We consider some other variants of ♣ as well.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 180 - 198
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1]Abraham, U., Rubin, M., and Shelah, S., On the consistency of some partition theorems for continuous colorings, and the structure of ℵ1-dense real order types, Annals of Pure and Applied Logic, vol. 29 (1985), pp. 123–206.CrossRefGoogle Scholar
[2]Fuchino, S., Shelah, S., and Soukup, L., Sticks and clubs, preprint.Google Scholar
[3]Jensen, R. B., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308.CrossRefGoogle Scholar
[4]Juhász, I., A weakening of ♣, with applications to topology, Commentationes Mathematicae Universitae Carolinae, vol. 29 (1988), no. 4, pp. 767–773.Google Scholar
[5]Komjáth, P., Set systems with finite chromatic number, European Journal of Combinatorics, vol. 10 (1989), pp. 543–549.CrossRefGoogle Scholar
[6]Kunen, K., Set theory, an introduction to independence proofs, North-Holland, Amsterdam, 1980.Google Scholar
[7]Ostaszewski, A. J., On countably compact perfectly normal spaces, Journal of London Mathematical Society, vol. 2 (1975), no. 14, pp. 505–516.Google Scholar
[8]Rajagopalan, M., Compact C-spaces and S-spaces, General topology and its relations to modern analysis and algebra IV, Proceedings of the fourth Prague topological symposium, 1976, Part A: Invited papers (Novák, J., editor), Lecture Notes in Mathematics, vol. 609, Springer-Verlag, 1977, pp. 179–189.Google Scholar
[9]Shelah, S., Proper and improper forcing, Perspectives in Mathematical Logic, Springer-Verlag, accepted.Google Scholar
[10]Shelah, S., Whitehead groups may not be free, even assuming CH, II, Israel Journal of Mathematics, vol. 35 (1980), pp. 257–285.CrossRefGoogle Scholar