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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
- 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
- Partitioning the club guessing January 22, 2014

### Keywords

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

# 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