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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

### Keywords

Generalized Clubs Singular Density Cohen real Aronszajn tree Singular cardinals combinatorics Club Guessing Hedetniemi's conjecture Knaster 05A17 Stevo Todorcevic Parameterized proxy principle Prevalent singular cardinals Selective Ultrafilter Absoluteness Square-Brackets Partition Relations Non-saturation Universal Sequences Rock n' Roll projective Boolean algebra Singular Cofinality Poset Erdos-Hajnal graphs very good scale reflection principles Reduced Power weak square sap Partition Relations incompactness P-Ideal Dichotomy HOD S-Space stationary reflection Rainbow sets Diamond Large Cardinals 05D10 Hereditarily Lindelöf space polarized partition relation Ostaszewski square OCA Cardinal function Chromatic number Kurepa Hypothesis Fodor-type reflection L-space Forcing Axioms xbox Successor of Singular Cardinal Successor of Regular Cardinal diamond star Almost countably chromatic Shelah's Strong Hypothesis Cardinal Invariants Almost Souslin Fast club Antichain approachability ideal Forcing Weakly compact cardinal b-scale 11P99 PFA Singular coﬁnality Axiom R stationary hitting Almost-disjoint famiy Chang's conjecture PFA(S)[S] Minimal Walks Sakurai's Bell inequality Commutative cancellative semigroups tensor product graph Uniformization Jonsson cardinal ccc Erdos Cardinal square Small forcing 20M14 Hindman's Theorem Ascent Path weak diamond Souslin Tree Martin's Axiom free Boolean algebra coloring number Fat stationary set Whitehead Problem Foundations Rado's conjecture Constructible Universe Coherent tree Dushnik-Miller Mandelbrot set middle diamond Microscopic Approach Prikry-type forcing Slim 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 Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, square, xbox
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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