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### 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

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

# 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