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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

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

# 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