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### 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

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

# 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