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