### 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

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