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- 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
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013

### Keywords

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