### Archives

### 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

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

# 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