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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

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

# 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