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- 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
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- Syndetic colorings with applications to S and L October 26, 2013
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### Keywords

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

# 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