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Ramsey theory over partitions nonmeager set Rado's conjecture super-Souslin tree Forcing with side conditions Forcing square principles Generalized Clubs Singular cardinals combinatorics Iterated forcing Subadditive Luzin set Entangled linear order Selective Ultrafilter Minimal Walks Postprocessing function Nonspecial tree Almost Souslin very good scale Small forcing Chang's conjecture Precaliber Non-saturation Diamond Martin's Axiom Filter reflection S-Space Rock n' Roll perfectly normal Erdos Cardinal Ineffable cardinal stick Knaster and friends projective Boolean algebra Subnormal ideal indecomposable filter Weakly compact cardinal C-sequence Local Club Condensation. higher Baire space Strong coloring Kurepa Hypothesis stationary reflection Parameterized proxy principle Knaster Forcing Axioms Chromatic number Interval topology on trees Prikry-type forcing coloring number Amenable C-sequence tensor product graph Countryman line xbox Vanishing levels Strongly compact cardinal Greatly Mahlo O-space Axiom R Successor of Singular Cardinal Constructible Universe Uniformly coherent GMA Hedetniemi's conjecture Antichain Closed coloring Reduced Power PFA(S)[S] Subtle cardinal Sakurai's Bell inequality Ulam matrix Souslin Tree Slim tree Aronszajn tree Ostaszewski square Coherent tree positive partition relation Fat stationary set Hereditarily Lindelöf space P-Ideal Dichotomy Partition Relations Erdos-Hajnal graphs Commutative cancellative semigroups Ascending path Prevalent singular cardinals OCA Sigma-Prikry Respecting tree Well-behaved magma Lipschitz reduction Cohen real Foundations Cardinal Invariants 54G20 Ascent Path Subtle tree property AIM forcing middle diamond full tree unbounded function diamond star Diamond for trees Cardinal function strongly bounded groups polarized partition relation approachability ideal reflection principles countably metacompact free Souslin tree free Boolean algebra Poset Microscopic Approach transformations Rainbow sets Singular Density PFA Fast club Strongly Luzin set regressive Souslin tree b-scale L-space specializable Souslin tree Monotonically far Mandelbrot set Fodor-type reflection sap Diamond-sharp Uniformly homogeneous ccc Distributive tree Commutative projection system Analytic sets Square-Brackets Partition Relations Open Access Successor of Regular Cardinal Partition relations for trees Dowker space HOD Almost-disjoint family weak diamond weak Kurepa tree Was Ulam right? Reflecting stationary set Generalized descriptive set theory ZFC construction stationary hitting Club Guessing Universal Sequences Singular cofinality incompactness Whitehead Problem square Large Cardinals Sierpinski's onto mapping principle Intersection model club_AD Dushnik-Miller Hindman's Theorem weak square Absoluteness Jonsson cardinal SNR Uniformization Almost countably chromatic Shelah's Strong Hypothesis
Tag Archives: Ascent Path
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
2 Comments
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Answering a question of Ketonen from the late 1970’s, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing … Continue reading
Squares, ultrafilters and forcing axioms
Joint work with Chris Lambie-Hanson and Jing Zhang. Abstract. We study the interplay of the three families of combinatorial objects or principles. Specifically, we show the following. Strong forcing axioms, in general incompatible with the existence of indexed squares, can … 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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Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa$, the existence … Continue reading
A microscopic approach to Souslin-tree constructions. Part II
Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
