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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

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

# 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