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

# 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