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- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

### Keywords

Prevalent singular cardinals Aronszajn tree Hereditarily Lindelöf space sap Club Guessing Diamond b-scale incompactness Erdos-Hajnal graphs Almost-disjoint famiy L-space ccc Erdos Cardinal projective Boolean algebra square Rock n' Roll Hedetniemi's conjecture Successor of Regular Cardinal Singular Cofinality weak diamond Rado's conjecture Generalized Clubs Knaster Dushnik-Miller Partition Relations Almost countably chromatic P-Ideal Dichotomy Antichain stationary hitting Almost Souslin Cardinal Invariants Small forcing Cardinal function Singular cardinals combinatorics Axiom R Prikry-type forcing Microscopic Approach Weakly compact cardinal Square-Brackets Partition Relations very good scale Whitehead Problem approachability ideal Uniformization middle diamond weak square Forcing Successor of Singular Cardinal Chromatic number Reduced Power PFA(S)[S] Rainbow sets Poset reflection principles stationary reflection Non-saturation polarized partition relation Absoluteness PFA Minimal Walks Kurepa Hypothesis Cohen real Singular Density Martin's Axiom Foundations diamond star Selective Ultrafilter Souslin Tree Shelah's Strong Hypothesis Constructible Universe tensor product graph Universal Sequences Singular coﬁnality Forcing Axioms Large Cardinals Sakurai's Bell inequality OCA S-Space free Boolean algebra Mandelbrot set Ascent Path Ostaszewski square

# Tag Archives: diamond star

## Square with built-in diamond-plus

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

Posted in Preprints, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, square
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## A Kurepa tree from diamond-plus

Recall that $T$ is said to be a $\kappa$-Kurepa tree if $T$ is a tree of height $\kappa$, whose levels $T_\alpha$ has size $\le|\alpha|$ for co-boundedly many $\alpha<\kappa$, and such that the set of branches of $T$ has size $>\kappa$. … Continue reading

## Jensen’s diamond principle and its relatives

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

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

Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading