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