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

# 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