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

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