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### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- 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

### Keywords

approachability ideal Chromatic number Kurepa Hypothesis Almost Souslin Sakurai's Bell inequality Almost countably chromatic Mandelbrot set sap b-scale polarized partition relation Absoluteness Ascent Path incompactness Weakly compact cardinal Prevalent singular cardinals Non-saturation weak diamond Singular Cofinality Singular coﬁnality L-space Souslin Tree weak square Prikry-type forcing Slim tree Shelah's Strong Hypothesis Martin's Axiom Selective Ultrafilter ccc Generalized Clubs diamond star Antichain Foundations Rainbow sets Coherent tree Singular cardinals combinatorics P-Ideal Dichotomy Dushnik-Miller tensor product graph Hindman's Theorem projective Boolean algebra Rado's conjecture Forcing free Boolean algebra Knaster square Ostaszewski square 05D10 Whitehead Problem Diamond Aronszajn tree PFA(S)[S] HOD Minimal Walks Parameterized proxy principle 20M14 Club Guessing Stevo Todorcevic Cardinal Invariants Small forcing Uniformization very good scale Constructible Universe Microscopic Approach PFA Singular Density Fat stationary set Fast club Successor of Regular Cardinal 05A17 stationary reflection Hereditarily Lindelöf space Large Cardinals middle diamond Successor of Singular Cardinal Cohen real Rock n' Roll Universal Sequences 11P99 Axiom R Erdos Cardinal S-Space reflection principles Partition Relations Commutative cancellative semigroups Poset Almost-disjoint famiy Forcing Axioms Square-Brackets Partition Relations Hedetniemi's conjecture Erdos-Hajnal graphs stationary hitting OCA Reduced Power Cardinal function

# 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

## 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