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