Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-09T01:49:52.592Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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]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