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