### 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

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

# Tag Archives: Non-saturation

## 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

## On guessing generalized clubs at the successors of regulars

Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading