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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

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

# 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