Rectangular square-bracket operation for successor of regular cardinals

Posted on April 11, 2012 by Assaf Rinot in categories: Partition Relations, Publications.

Joint work with Stevo Todorcevic.

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

In 1990, Shelah proved the above for $λ > 2^{ℵ_{0}}$ ;
In 1991, Shelah proved the above for $λ > ℵ_{1}$ ;
In 1997, Shelah proved the above for $λ = ℵ_{1}$ ;
In 2006, Moore proved the above for $λ = ℵ_{0}$ .

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

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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.

This entry was posted in Partition Relations, Publications and tagged 03E02, Minimal Walks, Square-Brackets Partition Relations, Successor of Regular Cardinal, ZFC construction. Bookmark the permalink.

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

Richard Dedekind says:

April 14, 2012 at 7:50 pm

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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saf says:

December 18, 2012 at 8:29 am

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

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