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