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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

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

# 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