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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
- Generalizations 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

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

# 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