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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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