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