Archives
Keywords
Intersection model Subnormal ideal HOD free Boolean algebra Reflecting stationary set Coherent tree Cohen real Erdos-Hajnal graphs incompactness Shelah's Strong Hypothesis club_AD Axiom R PFA Luzin set Strongly Luzin set positive partition relation Prevalent singular cardinals Ascent Path Mandelbrot set Foundations GMA Successor of Regular Cardinal projective Boolean algebra Uniformly homogeneous Dushnik-Miller Constructible Universe Amenable C-sequence Subadditive Successor of Singular Cardinal b-scale strongly bounded groups weak square O-space Strong coloring xbox C-sequence Cardinal function Fodor-type reflection Interval topology on trees sap Rock n' Roll 54G20 Lipschitz reduction Greatly Mahlo Ineffable cardinal Subtle tree property SNR Diamond for trees Parameterized proxy principle Jonsson cardinal Generalized descriptive set theory Uniformization Martin's Axiom Absoluteness Diamond Open Access Subtle cardinal Diamond-sharp higher Baire space approachability ideal OCA very good scale Square-Brackets Partition Relations Kurepa Hypothesis Singular cardinals combinatorics super-Souslin tree perfectly normal Closed coloring Uniformly coherent Vanishing levels Partition relations for trees Singular cofinality Sakurai's Bell inequality nonmeager set AIM forcing free Souslin tree Monotonically far Almost Souslin stationary hitting Non-saturation Commutative cancellative semigroups specializable Souslin tree Respecting tree Antichain Sierpinski's onto mapping principle Singular Density P-Ideal Dichotomy Cardinal Invariants Ramsey theory over partitions Hereditarily Lindelöf space reflection principles Knaster and friends Fast club square Filter reflection Iterated forcing Rado's conjecture middle diamond L-space unbounded function Large Cardinals weak diamond Whitehead Problem countably metacompact Ostaszewski square transformations Dowker space S-Space Aronszajn tree Rainbow sets regressive Souslin tree diamond star Chang's conjecture Poset PFA(S)[S] Commutative projection system Slim tree Reduced Power full tree Local Club Condensation. Entangled linear order Ulam matrix Club Guessing ZFC construction Microscopic Approach Almost countably chromatic Hedetniemi's conjecture Generalized Clubs indecomposable filter Nonspecial tree polarized partition relation Analytic sets Small forcing weak Kurepa tree Well-behaved magma Selective Ultrafilter Fat stationary set Forcing with side conditions Strongly compact cardinal Partition Relations Knaster Universal Sequences Precaliber stick Prikry-type forcing tensor product graph Almost-disjoint family Was Ulam right? ccc Weakly compact cardinal Erdos Cardinal Countryman line Ascending path Postprocessing function square principles Forcing Axioms Distributive tree stationary reflection Forcing Chromatic number Souslin Tree Hindman's Theorem Sigma-Prikry coloring number Minimal Walks
Tag Archives: C-sequence
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
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … 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
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Kurepa Hypothesis, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right?
2 Comments
Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … 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
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
11th Young Set Theory Workshop, June 2018
I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading
Posted in Invited Talks
Tagged Aronszajn tree, C-sequence, incompactness, Knaster, Minimal Walks, Postprocessing function, square
Leave a comment
