### 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
- 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
- Partitioning the club guessing January 22, 2014

### Keywords

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

# 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