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