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