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- 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
- Walk on countable ordinals: the characteristics December 1, 2013

### Keywords

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

# 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