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- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- 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
- Universal binary sequences November 14, 2013

### Keywords

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

# Tag Archives: stationary hitting

## 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