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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

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

# 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