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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
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- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
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### Keywords

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

# 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