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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

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

# 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