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