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Hedetniemi's conjecture Ineffable cardinal ccc Martin's Axiom projective Boolean algebra Almost-disjoint family Hindman's Theorem Intersection model Generalized Clubs AIM forcing Closed coloring Poset coloring number Erdos Cardinal Sakurai's Bell inequality Coherent tree Fodor-type reflection 54G20 free Souslin tree Universal Sequences Entangled linear order Partition relations for trees Partition Relations Strongly compact cardinal Axiom R Forcing Axioms Absoluteness O-space Parameterized proxy principle diamond star Diamond-sharp Generalized descriptive set theory Singular cardinals combinatorics Ascending path Selective Ultrafilter Postprocessing function Dowker space Square-Brackets Partition Relations approachability ideal Hereditarily Lindelöf space Vanishing levels P-Ideal Dichotomy sap Mandelbrot set Diamond unbounded function Precaliber specializable Souslin tree Cardinal Invariants Iterated forcing Antichain Weakly compact cardinal weak diamond Jonsson cardinal Uniformly coherent Was Ulam right? stationary reflection Countryman line Cohen real Small forcing Uniformization Dushnik-Miller higher Baire space very good scale Forcing with side conditions stick positive partition relation Open Access Greatly Mahlo Fat stationary set Cardinal function Subnormal ideal Local Club Condensation. polarized partition relation Ascent Path Chang's conjecture Ramsey theory over partitions super-Souslin tree incompactness Rado's conjecture Subtle cardinal middle diamond Well-behaved magma Baumgartner's square Shelah's Strong Hypothesis SNR Sigma-Prikry Large Cardinals C-sequence HOD perfectly normal Successor of Singular Cardinal Strongly Luzin set tensor product graph Rock n' Roll Successor of Regular Cardinal nonmeager set Filter reflection Knaster and friends full tree Reduced Power Uniformly homogeneous Interval topology on trees Lipschitz reduction Amenable C-sequence Chromatic number OCA Commutative cancellative semigroups Singular Density Singular cofinality regressive Souslin tree weak square Strong coloring Reflecting stationary set Subtle tree property Souslin Tree Ostaszewski square free Boolean algebra Foundations Ulam matrix ZFC construction Analytic sets Diamond for trees Slim tree PFA(S)[S] stationary hitting Subadditive Aronszajn tree Microscopic Approach b-scale Monotonically far Prevalent singular cardinals square principles Respecting tree weak Kurepa tree L-space indecomposable filter Kurepa Hypothesis GMA Commutative projection system Almost Souslin transformations Luzin set countably metacompact PFA Knaster Forcing Prikry-type forcing square Constructible Universe Club Guessing Fast club reflection principles Rainbow sets Distributive tree xbox club_AD Minimal Walks Sierpinski's onto mapping principle Almost countably chromatic strongly bounded groups Whitehead Problem Erdos-Hajnal graphs S-Space Nonspecial tree Non-saturation
Tag Archives: Vanishing levels
A new model for all C-sequences are trivial
Joint work with Zhixing You and Jiachen Yuan. Abstract. We construct a model in which all C-sequences are trivial, yet there exists a $\kappa$-Souslin tree with full vanishing levels. This answers a question from a previous paper, and provides an … Continue reading
Posted in Compactness, Publications
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, Subtle tree property, Vanishing levels
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Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Posted in Basis problems, Partition Relations, Preprints
Tagged Aronszajn tree, Ascending path, Club Guessing, Countryman line, Entangled linear order, Minimal Walks, Monotonically far, Partition relations for trees, Strong coloring, Subtle tree property, Vanishing levels, ZFC construction
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The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. This is an invariant in the … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, Ascent Path, C-sequence, Coherent tree, Dowker space, Open Access, Parameterized proxy principle, regressive Souslin tree, Respecting tree, Subtle tree property, Uniformly homogeneous, Vanishing levels, weak Kurepa tree
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