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### Recent blog posts

- More notions of forcing 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

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

# 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