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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
- Universal binary sequences November 14, 2013
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- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

### Keywords

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

# 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