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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

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

# 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