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