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