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