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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
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

### Keywords

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

# 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