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Successors of singular cardinals and coloring theorems I

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Abstract.

We investigate the existence of strong colorings on successors of singular cardinals. This work continues Section 2 of [1], but now our emphasis is on finding colorings of pairs of ordinals, rather than colorings of finite sets of ordinals.

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References

  1. Shelah, S.: More Jonsson algebras. Archive for Mathematical Logic 42 (2003), no.1, 1–44.

  2. Shelah, S.: Cardinal arithmetic. Oxford Logic Guides, vol. 29, Oxford University Press, 1994

  3. Shelah, S.: Jonsson Algebras in an inaccessible λ not λ-Mahlo. Cardinal Arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, 1994

  4. Shelah, S.: There are Jonsson algebras in many inaccessible cardinals. Cardinal Arithmetic, Oxford Logic Guides, vol. 29 Oxford University Press, 1994

  5. Shelah, S.: Proper and improper forcing. Perspectives in Mathematical Logic, Springer, 1998

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Authors and Affiliations

  1. Department of Mathematics, University of Northern Iowa, Cedar Falls, IA, 50614, USA

    Todd Eisworth

  2. Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel

    Saharon Shelah

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  1. Todd Eisworth
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  2. Saharon Shelah
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Correspondence to Todd Eisworth.

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This is publication number 535 of the second author.

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Eisworth, T., Shelah, S. Successors of singular cardinals and coloring theorems I. Arch. Math. Logic 44, 597–618 (2005). https://doi.org/10.1007/s00153-004-0258-7

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  • DOI: https://doi.org/10.1007/s00153-004-0258-7

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