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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

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

# 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