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- More notions of forcing 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

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

# 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