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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
- Generalizations 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

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

# 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