### Archives

### Recent blog posts

- More notions of forcing 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

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

# 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