Journal of Symbolic Logic

Successors of singular cardinals and coloring theorems {II}

Todd Eisworth and Saharon Shelah

Source: J. Symbolic Logic Volume 74, Issue 4 (2009), 1287-1309.

Abstract

In this paper, we investigate the extent to which techniques used in [10], [2], and [3]—developed to prove coloring theorems at successors of singular cardinals of uncountable cofinality—can be extended to cover the countable cofinality case.

Primary Subjects: 03E02
Keywords: square-brackets partition relations; minimal walks; successor of singular cardinal

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jsl/1254748692
Digital Object Identifier: doi:10.2178/jsl/1254748692

References

James E. Baumgarter, A new class of order-types, Annals of Pure and Applied Logic, vol. 54 (1991), no. 3, pp. 195--227.
T. Eisworth and S. Shelah, Successors of singular cardinals and coloring theorems I, Archive for Mathematical Logic, vol. 44 (2005), no. 5, pp. 597--618.
Mathematical Reviews (MathSciNet): MR2210148
Zentralblatt MATH: 1085.03035
Digital Object Identifier: doi:10.1007/s00153-004-0258-7
Todd Eisworth, A note on strong negative partition relations, Fundamenta Mathematicae, vol. 202 (2009), pp. 97--123.
Mathematical Reviews (MathSciNet): MR2506189
Zentralblatt MATH: 1168.03034
Digital Object Identifier: doi:10.4064/fm202-2-1
--------, Successors of singular cardinals, Handbook of set theory (Matthew Foreman and Akihiro Kanamori, editors), vol. II, Springer,forthcoming.
--------, Club-guessing, stationary reflection, and coloring theorems, Annals of Pure and Applied Logic, submitted.
P. Erdős, A. Hajnal, and R. Rado, Partition relations for cardinal numbers, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 16 (1965), pp. 93--196.
Mathematical Reviews (MathSciNet): MR202613
Zentralblatt MATH: 0158.26603
Digital Object Identifier: doi:10.1007/BF01886396
Menachem Kojman, The ABC of PCF, unpublished manuscript.
Saharon Shelah, On successors of singular cardinals, Logic Colloquium '78 (Mons, 1978), Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam, 1979, pp. 357--380.
Mathematical Reviews (MathSciNet): MR567680
Zentralblatt MATH: 0449.03045
--------, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, 1994.
Mathematical Reviews (MathSciNet): MR1318912
--------, There are Jonsson algebras in many inaccessible cardinals, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, 1994, Chapter III.
Stevo Todorčević, Partitioning pairs of countable ordinals, Acta Mathematica, vol. 159 (1987), no. 3--4, pp. 261--294.
Mathematical Reviews (MathSciNet): MR908147
Zentralblatt MATH: 0658.03028
Digital Object Identifier: doi:10.1007/BF02392561
--------, Walks on ordinals and their characteristics, Progress in Mathematics, vol. 263, Birkhauser, 2007.
Mathematical Reviews (MathSciNet): MR2355670
Zentralblatt MATH: 1148.03004
--------, Coherent sequences, Handbook of set theory (Matthew Foreman and Akihiro Kanamori, editors), vol. I, Springer,forthcoming.

2009 © Association for Symbolic Logic