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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

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

# 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