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