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### Keywords

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

# 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