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