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