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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

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

# 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