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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

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