Archives
Keywords
Uniformly homogeneous S-Space coloring number tensor product graph Successor of Regular Cardinal Iterated forcing Subtle tree property Subnormal ideal sap middle diamond Partition Relations Jonsson cardinal 54G20 Generalized Clubs free Souslin tree regressive Souslin tree Poset Amenable C-sequence PFA AIM forcing Absoluteness Shelah's Strong Hypothesis Coherent tree Slim tree Large Cardinals xbox indecomposable ultrafilter specializable Souslin tree polarized partition relation Dushnik-Miller Antichain Nonspecial tree Axiom R Singular cofinality stationary reflection Reduced Power Erdos-Hajnal graphs approachability ideal weak diamond Ostaszewski square Parameterized proxy principle unbounded function Kurepa Hypothesis Martin's Axiom PFA(S)[S] Generalized descriptive set theory Greatly Mahlo Chang's conjecture Diamond for trees ZFC construction Forcing Closed coloring SNR Erdos Cardinal reflection principles Ineffable cardinal Fat stationary set Analytic sets Cohen real Sierpinski's onto mapping principle Vanishing levels strongly bounded groups Fast club Hindman's Theorem Ulam matrix Prevalent singular cardinals P-Ideal Dichotomy full tree Was Ulam right Singular cardinals combinatorics C-sequence very good scale countably metacompact HOD Uniformization square principles Postprocessing function Subadditive Reflecting stationary set Singular Density Lipschitz reduction OCA nonmeager set Almost Souslin Knaster and friends Ascent Path Knaster Commutative cancellative semigroups super-Souslin tree Distributive tree higher Baire space Dowker space Prikry-type forcing Minimal Walks Foundations projective Boolean algebra ccc Luzin set Well-behaved magma Souslin Tree Local Club Condensation. Square-Brackets Partition Relations Cardinal function Weakly compact cardinal diamond star Filter reflection Mandelbrot set Selective Ultrafilter Aronszajn tree Strongly Luzin set free Boolean algebra b-scale Almost-disjoint family Almost countably chromatic Diamond Rainbow sets Cardinal Invariants Constructible Universe stick transformations incompactness Precaliber stationary hitting club_AD Hereditarily Lindelöf space Small forcing Rado's conjecture Sakurai's Bell inequality Club Guessing GMA Chromatic number Whitehead Problem Fodor-type reflection positive partition relation Subtle cardinal Diamond-sharp Strong coloring Universal Sequences Open Access O-space Forcing Axioms Microscopic Approach Rock n' Roll Sigma-Prikry weak Kurepa tree square Hedetniemi's conjecture L-space Uniformly coherent Successor of Singular Cardinal weak square Ramsey theory over partitions Non-saturation
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