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Prikry-type forcing Souslin Tree Minimal Walks SNR Ulam matrix Hindman's Theorem Axiom R Reduced Power C-sequence Local Club Condensation. Almost Souslin Vanishing levels Ascending path Fodor-type reflection Jonsson cardinal Rado's conjecture Singular cardinals combinatorics Intersection model Cardinal function Forcing Commutative cancellative semigroups Kurepa Hypothesis L-space Hedetniemi's conjecture tensor product graph Fast club Fat stationary set Generalized Clubs Strongly compact cardinal Subnormal ideal Amenable C-sequence positive partition relation Singular cofinality Forcing Axioms Subtle tree property polarized partition relation 54G20 S-Space Respecting tree reflection principles Almost-disjoint family Subtle cardinal Closed coloring Entangled linear order strongly bounded groups Successor of Singular Cardinal Selective Ultrafilter Microscopic Approach projective Boolean algebra Ramsey theory over partitions O-space Square-Brackets Partition Relations stick xbox Sierpinski's onto mapping principle Precaliber Partition Relations free Souslin tree Prevalent singular cardinals AIM forcing Non-saturation sap Whitehead Problem Open Access indecomposable filter Uniformization Poset Club Guessing Knaster Martin's Axiom Foundations Shelah's Strong Hypothesis Well-behaved magma Ascent Path GMA Almost countably chromatic Sigma-Prikry Absoluteness perfectly normal Small forcing Erdos Cardinal PFA Sakurai's Bell inequality transformations P-Ideal Dichotomy Slim tree Ostaszewski square Diamond-sharp square principles Constructible Universe Nonspecial tree Universal Sequences Cohen real Generalized descriptive set theory Iterated forcing nonmeager set Diamond Erdos-Hajnal graphs diamond star Interval topology on trees unbounded function Diamond for trees regressive Souslin tree Uniformly coherent Hereditarily Lindelöf space b-scale Singular Density Chromatic number approachability ideal weak Kurepa tree Countryman line Coherent tree Distributive tree very good scale Subadditive weak square Rainbow sets Mandelbrot set full tree Aronszajn tree PFA(S)[S] ccc Analytic sets Lipschitz reduction Large Cardinals coloring number Parameterized proxy principle Rock n' Roll HOD Uniformly homogeneous middle diamond Greatly Mahlo OCA specializable Souslin tree Cardinal Invariants free Boolean algebra ZFC construction countably metacompact Chang's conjecture Strong coloring higher Baire space Was Ulam right? Luzin set Antichain stationary reflection Monotonically far Postprocessing function square Strongly Luzin set Successor of Regular Cardinal Ineffable cardinal incompactness Knaster and friends super-Souslin tree Commutative projection system Filter reflection Dushnik-Miller Reflecting stationary set weak diamond Weakly compact cardinal Forcing with side conditions club_AD Dowker space stationary hitting
Tag Archives: Vanishing levels
A new model for all C-sequences are trivial
Joint work with Zhixing You and Jiachen Yuan. Abstract. We construct a model in which all C-sequences are trivial, yet there exists a $\kappa$-Souslin tree with full vanishing levels. This answers a question from a previous paper, and provides an … Continue reading
Posted in Compactness, Publications
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, Subtle tree property, Vanishing levels
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Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
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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