### 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

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

# Tag Archives: Successor of Regular Cardinal

## Rectangular square-bracket operation for successor of regular cardinals

Joint work with Stevo Todorcevic. Extended Abstract: Consider the coloring statement $\lambda^+\nrightarrow[\lambda^+;\lambda^+]^2_{\lambda^+}$ for a given regular cardinal $\lambda$: In 1990, Shelah proved the above for $\lambda>2^{\aleph_0}$; In 1991, Shelah proved the above for $\lambda>\aleph_1$; In 1997, Shelah proved the above … 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