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