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