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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

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

# Tag Archives: diamond star

## 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

Posted in Open Problems, Publications
Tagged 03E05, 03E35, 03E50, approachability ideal, Club Guessing, Diamond, diamond star, Non-saturation, sap, Souslin Tree, square, stationary hitting, Uniformization, Whitehead Problem
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## 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