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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

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

# 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