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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- 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

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Almost countably chromatic Commutative cancellative semigroups S-Space Knaster Hedetniemi's conjecture 20M14 Singular Density Mandelbrot set Stevo Todorcevic Slim tree polarized partition relation Large Cardinals Ostaszewski square free Boolean algebra OCA P-Ideal Dichotomy Forcing Uniformization Sakurai's Bell inequality Forcing Axioms Diamond Successor of Regular Cardinal Hereditarily Lindelöf space ccc PFA Partition Relations Chang's conjecture square b-scale Axiom R Singular Cofinality Antichain HOD Poset incompactness Chromatic number Erdos Cardinal Club Guessing Singular coﬁnality Jonsson cardinal Foundations Souslin Tree Universal Sequences Cardinal Invariants Coherent tree tensor product graph approachability ideal Martin's Axiom Prevalent singular cardinals Cohen real Whitehead Problem L-space Rainbow sets Almost-disjoint famiy Generalized Clubs Singular cardinals combinatorics projective Boolean algebra Parameterized proxy principle Rado's conjecture Erdos-Hajnal graphs Microscopic Approach Shelah's Strong Hypothesis very good scale weak diamond sap 05D10 Fat stationary set Almost Souslin stationary hitting Hindman's Theorem stationary reflection Minimal Walks PFA(S)[S] 05A17 Reduced Power diamond star Square-Brackets Partition Relations reflection principles middle diamond Absoluteness Kurepa Hypothesis Weakly compact cardinal Fast club Prikry-type forcing Non-saturation Successor of Singular Cardinal Cardinal function Constructible Universe Ascent Path Selective Ultrafilter Small forcing Dushnik-Miller 11P99 Rock n' Roll weak square Aronszajn tree

# 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