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