### 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

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

# Tag Archives: sap

## 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

## The failure of diamond on a reflecting stationary set

Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … 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