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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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