Hostname: page-component-7dd5485656-tbj44 Total loading time: 0 Render date: 2025-10-30T22:15:34.775Z Has data issue: false hasContentIssue false
  • English
  • Français

Simultaneous reflection and impossible ideals

Published online by Cambridge University Press:  12 March 2014

Todd Eisworth
Todd Eisworth*
Affiliation:
Department of Mathematics, Ohio University, Athens, OH 45701, USA, E-mail: eisworth@math.ohiou.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that if holds for a singular cardinal μ, then any collection of fewer than cf(μ) stationary subsets of μ+ must reflect simultaneously.

Keywords

minimal walksstationary reflectionsquare-brackets partition relationssuccessors of singular cardinals

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1325 - 1338
Copyright
Copyright © Association for Symbolic Logic 2012

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Eisworth, Todd, A note on strong negative partition relations, Fundamenta Mathematicae, vol. 202 (2009), pp. 97–123.CrossRefGoogle Scholar
[2]Eisworth, Todd, Getting more colors, this Journal, submitted, December 2009.Google Scholar
[3]Eisworth, Todd, Club-guessing, stationary reflection, and coloring theorems, Annals of Pure and Applied Logic, vol. 161 (2010), no. 10, pp. 1216–1243.CrossRefGoogle Scholar
[4]Eisworth, Todd, Successors of singular cardinals, Handbook of set theory (Foreman, M. and Kanamori, A., editors), vol. 2, Springer, Dordrecht, 2010, pp. 1229–1350.CrossRefGoogle Scholar
[5]Eisworth, Todd and Shelah, Saharon, Successors of singular cardinals and coloring theorems. II, this Journal, vol. 74 (2009), no. 4, pp. 1287–1309.Google Scholar
[6]Erdős, Paul, Hajnal, András, Máté, Attila, and Rado, Richard, Combinatorial set theory: partition relations for cardinals, Studies in Logic and the Foundations of Mathematics, vol. 106, North-Holland, Amsterdam, 1984.Google Scholar
[7]Foreman, Matthew and Kanamori, Akihiro (editors), Handbook of set theory, Springer, Dordrecht, 2010, 3 volumes.CrossRefGoogle Scholar
[8]Hajnal, András and Hamburger, Peter, Set theory, London Mathematical Society Student Texts, vol. 48, Cambridge University Press, Cambridge, 1999, Translated from the 1983 Hungarian original by Attila Máté.CrossRefGoogle Scholar
[9]Jech, Thomas, Stationary sets, Handbook of set theory (Foreman, M. and Kanamori, A., editors), vol. 1, Springer, Dordrecht, 2010, pp. 93–128.CrossRefGoogle Scholar
[10]Kanamori, Akihiro, The higher infinite, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1994.Google Scholar
[11]Rinot, Assaf, Transforming rectangles into squares, with applications to strong colorings, preprint.Google Scholar
[12]Shelah, Saharon, Was Sierpiński right! I, Israel Journal of Mathematics, vol. 62 (1988), no. 3, pp. 355–380.CrossRefGoogle Scholar
[13]Shelah, Saharon, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, 1994.CrossRefGoogle Scholar
[14]Todorčević, Stevo, Partitioning pairs of countable ordinals, Acta Mathematica, vol. 159 (1987), no. 3–4, pp. 261–294.CrossRefGoogle Scholar
[15]Todorcevic, Stevo, Walks on ordinals and their characteristics, Progress in Mathematics, vol. 263, Birkháuser Verlag, Basel, 2007.CrossRefGoogle Scholar