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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
- 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

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

# 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