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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

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

# 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