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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

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

# 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