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