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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
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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

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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