Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-30T00:27:46.774Z Has data issue: false hasContentIssue false
  • English
  • Français

REFLECTION OF STATIONARY SETS AND THE TREE PROPERTY AT THE SUCCESSOR OF A SINGULAR CARDINAL

Published online by Cambridge University Press:  23 January 2017

LAURA FONTANELLA  and
MENACHEM MAGIDOR
LAURA FONTANELLA
Affiliation:
HEBREW UNIVERSITY OF JERUSALEM EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS GIVAT RAM, 91904 JERUSALEM, ISRAELE-mail: laura.fontanella@mail.huji.ac.il
MENACHEM MAGIDOR
Affiliation:
HEBREW UNIVERSITY OF JERUSALEM EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS GIVAT RAM, 91904 JERUSALEM, ISRAELE-mail: mensara@savion.huji.ac.il
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that from infinitely many supercompact cardinals one can force a model of ZFC where both the tree property and the stationary reflection hold at אω2+1.

Keywords

03E05Reflection of stationary setstree propertylarge cardinals
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 272 - 291
Copyright
Copyright © The Association for Symbolic Logic 2017 

References

REFERENCES

Eklof, P., On the existence of κ free Abelian groups . Proceedings of the American Mathematical Society, vol. 47 (1975), pp. 65–72.Google Scholar
Kunen, K., Saturated ideals, this Journal, vol. 43 (1978), no. 1, pp. 65–76.Google Scholar
Laver, R., Making the supercompactness of κ indestructible under κ-directed closed forcing . Israel Journal of Mathematics, vol. 29 (1978), pp. 385–388.CrossRefGoogle Scholar
Magidor, M. and Shelah, S., The tree property at successors of singular cardinals . Archive for Mathematical Logic, vol. 35 (1996), no. 5–6, pp. 385–404.CrossRefGoogle Scholar
Magidor, M. and Shelah, S., When does almost free imply free? (For groups, transversals, etc.). Journal of the American Mathematical Society, vol. 7 (1994), no. 4, pp. 769–830.CrossRefGoogle Scholar
Mitchell, W. J., Aronszajn trees and the independence of the transfer property . Annals of Mathematical Logic, vol. 5 (1972), pp. 21–46.CrossRefGoogle Scholar
Neeman, I., The tree property up to א ω+1, this Journal, vol. 79 (2014), pp. 429–459.Google Scholar
Shelah, S., A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals . Israel Journal of Mathematics, vol. 21 (1975), pp. 319–339.CrossRefGoogle Scholar
Shelah, S., On successors of singular cardinals . Logic Colloquium (Boffa, M., Van Dallen, D., and McAloon, K., editors), Studies in Logic and the Foundations of Mathematics, vol. 78, North Holland, Amsterdam, 1979, pp. 357–380.Google Scholar
Sinapova, D., The tree property at א ω+1, this Journal, vol. 77 (2012), no. 1, pp. 279–290.Google Scholar
Unger, S., Fragility and indestructibility of the tree property . Archive for Mathematical Logic, vol. 51 (2012), no. 5–6, pp. 635–645.CrossRefGoogle Scholar