Tag Archives: diamond star

Square with built-in diamond-plus

Posted on October 1, 2015 by Assaf Rinot in categories: Publications, Squares and Diamonds.

Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in L for every infinite cardinal. As an application, we prove that … Continue reading →

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A Kurepa tree from diamond-plus

Posted on May 29, 2013 by Assaf Rinot in categories: Blog, Expository.

Recall that T is said to be a κ-Kurepa tree if T is a tree of height κ, whose levels Tα has size ≤|α| for co-boundedly many α<κ, and such that the set of branches of T has size >κ. … Continue reading →

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Jensen’s diamond principle and its relatives

Posted on October 6, 2011 by Assaf Rinot in categories: Open Problems, Publications, Squares and Diamonds.

This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading →

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A relative of the approachability ideal, diamond and non-saturation

Posted on September 27, 2011 by Assaf Rinot in categories: Publications, Squares and Diamonds.

Abstract: Let λ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that ◻λ∗ together with 2λ=λ+ implies ♢S for every S⊆λ+ that reflects stationarily often. In this paper, for a subset S⊂λ+, a normal subideal of … Continue reading →

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