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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

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