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Subnormal ideal diamond star Jonsson cardinal Uniformly coherent Analytic sets Postprocessing function Ulam matrix Closed coloring countably metacompact GMA Commutative cancellative semigroups very good scale approachability ideal Ineffable cardinal stationary reflection Whitehead Problem Chromatic number Generalized Clubs Cohen real Lipschitz reduction Kurepa Hypothesis Luzin set Diamond-sharp Sigma-Prikry Slim tree Reduced Power Ascent Path Souslin Tree Sierpinski's onto mapping principle stick stationary hitting Partition Relations square Amenable C-sequence O-space free Boolean algebra Strongly Luzin set higher Baire space Fodor-type reflection Parameterized proxy principle Chang's conjecture Local Club Condensation. Subadditive xbox coloring number Prikry-type forcing b-scale Poset P-Ideal Dichotomy Universal Sequences Well-behaved magma ZFC construction Small forcing Ramsey theory over partitions Vanishing levels Selective Ultrafilter weak Kurepa tree Antichain Singular cardinals combinatorics Hereditarily Lindelöf space Sakurai's Bell inequality Almost countably chromatic Open Access Aronszajn tree Large Cardinals AIM forcing Cardinal function reflection principles Fast club S-Space Weakly compact cardinal Intersection model Foundations Ostaszewski square Strong coloring Coherent tree specializable Souslin tree Shelah's Strong Hypothesis Dushnik-Miller Non-saturation Erdos Cardinal Rainbow sets club_AD Square-Brackets Partition Relations weak diamond Was Ulam right Reflecting stationary set Diamond Nonspecial tree Filter reflection Distributive tree Forcing Axioms Almost Souslin Singular cofinality Rado's conjecture Club Guessing Subtle cardinal Dowker space Rock n' Roll Precaliber middle diamond Minimal Walks incompactness Generalized descriptive set theory Mandelbrot set HOD free Souslin tree PFA unbounded function Uniformization L-space Hindman's Theorem Uniformly homogeneous 54G20 Almost-disjoint family C-sequence Respecting tree positive partition relation weak square sap strongly bounded groups Martin's Axiom Absoluteness ccc super-Souslin tree Greatly Mahlo Countryman line transformations Singular Density Commutative projection system full tree Successor of Regular Cardinal Fat stationary set SNR Knaster and friends square principles Forcing Strongly compact cardinal Subtle tree property Hedetniemi's conjecture nonmeager set Prevalent singular cardinals projective Boolean algebra regressive Souslin tree Erdos-Hajnal graphs Cardinal Invariants PFA(S)[S] indecomposable ultrafilter OCA Iterated forcing Successor of Singular Cardinal Diamond for trees polarized partition relation Axiom R Constructible Universe Knaster tensor product graph Microscopic Approach
Tag Archives: Greatly Mahlo
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … Continue reading
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
