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- 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

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

# 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