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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

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

# 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