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