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- 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
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### Keywords

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

# 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