### 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

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

# 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