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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

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

# 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