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 $\lambda$.

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**Citation information:**

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

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!

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Submitted to

Fundamenta Mathematicae, April 2012.Accepted, December 2012.

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