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Fast club Was Ulam right Slim tree Almost-disjoint family Diamond-sharp Singular cardinals combinatorics Postprocessing function Minimal Walks Prikry-type forcing regressive Souslin tree Successor of Singular Cardinal Ostaszewski square Souslin Tree ccc Rainbow sets 54G20 Antichain ZFC construction Dowker space Chromatic number Aronszajn tree Fodor-type reflection S-Space Coherent tree Almost Souslin Axiom R approachability ideal Sierpinski's onto mapping principle Reflecting stationary set Successor of Regular Cardinal SNR Reduced Power Rock n' Roll Diamond for trees Lipschitz reduction Dushnik-Miller Uniformization C-sequence Ramsey theory over partitions Uniformly homogeneous incompactness very good scale Forcing P-Ideal Dichotomy Greatly Mahlo PFA(S)[S] projective Boolean algebra Hereditarily Lindelöf space Rado's conjecture Iterated forcing Singular cofinality Knaster Nonspecial tree free Boolean algebra xbox Jonsson cardinal coloring number transformations stationary hitting Subtle tree property Precaliber stick AIM forcing Distributive tree Ulam matrix Whitehead Problem higher Baire space full tree GMA Parameterized proxy principle Vanishing levels Subtle cardinal weak Kurepa tree Singular Density Ascent Path Diamond Subadditive Weakly compact cardinal Kurepa Hypothesis club_AD Closed coloring Commutative cancellative semigroups square principles Luzin set Subnormal ideal PFA Sakurai's Bell inequality Hedetniemi's conjecture Universal Sequences Microscopic Approach Foundations Hindman's Theorem Fat stationary set Prevalent singular cardinals Martin's Axiom Chang's conjecture Mandelbrot set Local Club Condensation. Cardinal function Almost countably chromatic Selective Ultrafilter Well-behaved magma L-space nonmeager set Small forcing positive partition relation Cardinal Invariants super-Souslin tree Forcing Axioms O-space Erdos-Hajnal graphs Knaster and friends sap Shelah's Strong Hypothesis Poset Generalized Clubs diamond star Erdos Cardinal free Souslin tree Uniformly coherent polarized partition relation HOD weak diamond strongly bounded groups Absoluteness Generalized descriptive set theory Strongly Luzin set OCA Open Access Amenable C-sequence Strong coloring Constructible Universe Club Guessing Analytic sets Non-saturation square Large Cardinals Cohen real Filter reflection Partition Relations stationary reflection specializable Souslin tree Ineffable cardinal reflection principles weak square unbounded function indecomposable ultrafilter Square-Brackets Partition Relations countably metacompact tensor product graph middle diamond Sigma-Prikry b-scale
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 $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. The latter is an invariant in … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, C-sequence, Coherent tree, Parameterized proxy principle, regressive Souslin tree, Subtle tree property, Uniformly homogeneous, Vanishing levels
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A guessing principle from a Souslin tree, with applications to topology
Joint work with Roy Shalev. Abstract. We introduce a new combinatorial principle which we call $\clubsuit_{AD}$. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out … Continue reading
Posted in Publications, Souslin Hypothesis, Topology
Tagged club_AD, Dowker space, O-space, regressive Souslin tree, S-Space, Souslin Tree, Vanishing levels
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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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