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Getting more colors I

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 establish a coloring theorem for successors of singular cardinals, and use it prove that for any such cardinal μ, we have if and only if for arbitrarily large θ < μ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 1 - 16
Copyright
Copyright © Association for Symbolic Logic 2013

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References

REFERENCES

[1]Baumgartner, James E., A new class of order types, Annals of Pure and Applied Logic, vol. 9 (1976), no. 3, pp. 187–222.Google Scholar
[2]Cummings, James, Notes on singular cardinal combinatorics, Notre Dame Journal of Formal Logic, vol. 46 (2005), no. 3, pp. 251–282.CrossRefGoogle Scholar
[3]Eisworth, Todd, A note on strong negative partition relations, Fundamenta Mathematicae, vol. 202 (2009), pp. 97–123.CrossRefGoogle Scholar
[4]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
[5]Eisworth, Todd, Successors of singular cardinals, Handbook of set theory (Foreman, M. and Kanamori, A., editors), vol. 2, Springer, 2010, pp. 1229–1350.CrossRefGoogle Scholar
[6]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
[7]Erdős, P., Hajnal, A., and Rado, R., Partition relations for cardinal numbers, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 16 (1965), pp. 93–196.CrossRefGoogle Scholar
[8]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
[9]Shelah, Saharon, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, 1994.CrossRefGoogle Scholar
[10]Todorčević, Stevo, Partitioning pairs of countable ordinals, Acta Mathematica, vol. 159 (1987), no. 3–4, pp. 261–294.CrossRefGoogle Scholar
[11]Todorčević, Stevo, Walks on ordinals and their characteristics, Progress in Mathematics, vol. 263, Birkháuser Verlae, Basel, 2007.CrossRefGoogle Scholar