### 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

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

# 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