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Filter reflection Knaster and friends Absoluteness Jonsson cardinal ZFC construction Amenable C-sequence Singular Density Interval topology on trees polarized partition relation club_AD Reflecting stationary set positive partition relation Generalized Clubs full tree Almost-disjoint family sap Sigma-Prikry L-space Antichain 54G20 Partition Relations Hindman's Theorem Prevalent singular cardinals Fast club very good scale HOD Erdos-Hajnal graphs weak Kurepa tree Dushnik-Miller indecomposable filter Rado's conjecture weak square Large Cardinals stationary reflection Strong coloring Selective Ultrafilter Closed coloring projective Boolean algebra P-Ideal Dichotomy Vanishing levels Diamond Square-Brackets Partition Relations Martin's Axiom nonmeager set Knaster free Souslin tree super-Souslin tree coloring number Countryman line Precaliber Subnormal ideal Successor of Regular Cardinal tensor product graph Sierpinski's onto mapping principle Chang's conjecture stationary hitting Well-behaved magma Foundations Almost countably chromatic Ulam matrix Hereditarily Lindelöf space Ostaszewski square Ascent Path Postprocessing function Cardinal function PFA Souslin Tree OCA AIM forcing Dowker space Non-saturation Intersection model Greatly Mahlo Luzin set Uniformly coherent Strongly Luzin set Ineffable cardinal Uniformly homogeneous Prikry-type forcing Forcing Axioms Diamond for trees Subtle cardinal PFA(S)[S] higher Baire space Local Club Condensation. ccc Cardinal Invariants Entangled linear order Fat stationary set reflection principles Erdos Cardinal Singular cofinality Singular cardinals combinatorics Successor of Singular Cardinal Subadditive Kurepa Hypothesis free Boolean algebra Whitehead Problem Hedetniemi's conjecture Ramsey theory over partitions Constructible Universe specializable Souslin tree incompactness Axiom R Generalized descriptive set theory O-space Iterated forcing Club Guessing Diamond-sharp weak diamond Coherent tree Parameterized proxy principle Commutative cancellative semigroups Forcing regressive Souslin tree Minimal Walks Microscopic Approach Aronszajn tree Fodor-type reflection Small forcing Poset GMA SNR Open Access Sakurai's Bell inequality diamond star Rainbow sets Forcing with side conditions transformations Strongly compact cardinal b-scale S-Space perfectly normal Rock n' Roll Mandelbrot set Cohen real Weakly compact cardinal Distributive tree Nonspecial tree xbox square principles C-sequence Monotonically far countably metacompact Shelah's Strong Hypothesis Slim tree Analytic sets Commutative projection system Chromatic number Universal Sequences Subtle tree property Lipschitz reduction Was Ulam right? square Respecting tree approachability ideal stick Uniformization middle diamond Almost Souslin Reduced Power Ascending path strongly bounded groups unbounded function
Tag Archives: regressive Souslin tree
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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Higher Souslin trees and the GCH, revisited
Abstract. It is proved that for every uncountable cardinal $\lambda$, GCH+$\square(\lambda^+)$ entails the existence of a $\text{cf}(\lambda)$-complete $\lambda^+$-Souslin tree. In particular, if GCH holds and there are no $\aleph_2$-Souslin trees, then $\aleph_2$ is weakly compact in Godel’s constructible universe, improving … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, Open Access, regressive Souslin tree, Souslin Tree, square, Weakly compact cardinal, xbox
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