### 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

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

# 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