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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

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

# 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