### Archives

### 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

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

# 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