Rectangular square-bracket operation for successor of regular cardinals

Joint work with Stevo Todorcevic.

Extended Abstract: Consider the coloring statement $\lambda^+\nrightarrow[\lambda^+;\lambda^+]^2_{\lambda^+}$ for a given regular cardinal $\lambda$:

  • In 1990, Shelah proved the above for $\lambda>2^{\aleph_0}$;
  • In 1991, Shelah proved the above for $\lambda>\aleph_1$;
  • In 1997, Shelah proved the above for $\lambda=\aleph_1$;
  • In 2006, Moore proved the above for $\lambda=\aleph_0$.

In this paper, we provide a uniform proof of the fact that $\lambda^+\nrightarrow[\lambda^+;\lambda^+]^2_{\lambda^+}$ holds for every regular cardinal $\lambda$.

Downloads:

[No arXiv entry]

Citation information:

A. Rinot and S. Todorcevic, Rectangular square-bracket operation for successor of regular cardinals, Fund. Math., 220(2): 119-128, 2013.

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2 Responses to Rectangular square-bracket operation for successor of regular cardinals

  1. Richard Dedekind says:

    I am always impressed when someone improves Shelah’s results. Shelah is one of those people that always chase after improving their results, and relentlessly if I may add. Moore gaining on him is mighty impressive. Nice work uniformizing the proof, I will have to sit and read through this later this week!

       0 likes

  2. saf says:

    Submitted to Fundamenta Mathematicae, April 2012.
    Accepted, December 2012.

       0 likes

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