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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

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

# 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