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

# 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