### 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

Diamond Hedetniemi's conjecture Large Cardinals Almost countably chromatic Club Guessing P-Ideal Dichotomy weak square Knaster Erdos Cardinal Selective Ultrafilter Universal Sequences Shelah's Strong Hypothesis square Forcing Axioms Non-saturation Axiom R Almost Souslin Microscopic Approach Minimal Walks Hereditarily Lindelöf space Ostaszewski square approachability ideal Cardinal function polarized partition relation Singular Density xbox Forcing Aronszajn tree tensor product graph Parameterized proxy principle Stevo Todorcevic 05D10 Rado's conjecture Singular coﬁnality 05A17 Jonsson cardinal weak diamond 20M14 reflection principles 11P99 Prevalent singular cardinals OCA stationary hitting Weakly compact cardinal Cohen real Chang's conjecture L-space Hindman's Theorem Foundations Constructible Universe Sakurai's Bell inequality Souslin Tree Dushnik-Miller stationary reflection Absoluteness Fast club middle diamond sap incompactness Rock n' Roll Whitehead Problem ccc Antichain Square-Brackets Partition Relations HOD Erdos-Hajnal graphs diamond star Small forcing Partition Relations Commutative cancellative semigroups Ascent Path Cardinal Invariants Slim tree Martin's Axiom Poset projective Boolean algebra Generalized Clubs Singular Cofinality Successor of Singular Cardinal Reduced Power Chromatic number very good scale b-scale Prikry-type forcing S-Space Successor of Regular Cardinal Almost-disjoint famiy Uniformization Fodor-type reflection Rainbow sets Mandelbrot set Fat stationary set Kurepa Hypothesis coloring number free Boolean algebra Singular cardinals combinatorics PFA(S)[S] PFA Coherent tree

# 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