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Coherent tree S-Space Well-behaved magma Axiom R indecomposable ultrafilter middle diamond Open Access tensor product graph Small forcing Hindman's Theorem HOD Ostaszewski square Selective Ultrafilter Postprocessing function Almost Souslin Sigma-Prikry Almost-disjoint family weak Kurepa tree Parameterized proxy principle positive partition relation Mandelbrot set Uniformly homogeneous Partition Relations stationary hitting Distributive tree Poset Forcing Axioms Diamond regressive Souslin tree Greatly Mahlo stationary reflection PFA unbounded function Filter reflection Diamond-sharp countably metacompact Rado's conjecture Sierpinski's onto mapping principle Antichain Knaster polarized partition relation Souslin Tree sap Fodor-type reflection Hereditarily Lindelöf space club_AD ZFC construction projective Boolean algebra Dowker space Analytic sets Local Club Condensation. L-space Nonspecial tree Fat stationary set Ramsey theory over partitions Ineffable cardinal Kurepa Hypothesis Singular cofinality strongly bounded groups square approachability ideal Singular Density Shelah's Strong Hypothesis Prevalent singular cardinals Large Cardinals Ulam matrix Hedetniemi's conjecture Chang's conjecture Subtle tree property P-Ideal Dichotomy Successor of Regular Cardinal SNR Square-Brackets Partition Relations PFA(S)[S] square principles reflection principles Jonsson cardinal weak square Commutative cancellative semigroups Generalized Clubs GMA ccc higher Baire space specializable Souslin tree Dushnik-Miller Successor of Singular Cardinal nonmeager set Sakurai's Bell inequality Martin's Axiom coloring number Was Ulam right xbox Precaliber Reduced Power Erdos-Hajnal graphs transformations stick Universal Sequences Cardinal function free Souslin tree Cohen real super-Souslin tree Luzin set Subtle cardinal Weakly compact cardinal Subadditive Lipschitz reduction Minimal Walks Singular cardinals combinatorics Reflecting stationary set b-scale Uniformly coherent O-space Constructible Universe Rock n' Roll Forcing Amenable C-sequence Uniformization Cardinal Invariants free Boolean algebra Microscopic Approach Strong coloring Non-saturation Subnormal ideal weak diamond Chromatic number diamond star very good scale AIM forcing full tree Club Guessing Slim tree Aronszajn tree Prikry-type forcing Closed coloring Rainbow sets 54G20 C-sequence Vanishing levels Generalized descriptive set theory Knaster and friends Foundations Erdos Cardinal OCA Absoluteness Strongly Luzin set Whitehead Problem Diamond for trees Fast club Iterated forcing Ascent Path Almost countably chromatic incompactness
Tag Archives: C-sequence
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
Posted in Preprints, Souslin Hypothesis
Tagged C-sequence, free Souslin tree, Parameterized proxy principle, Souslin Tree, specializable Souslin tree, square principles, xbox
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The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. The latter is an invariant in … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, C-sequence, Coherent tree, Parameterized proxy principle, regressive Souslin tree, Subtle tree property, Uniformly homogeneous, Vanishing levels
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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, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right
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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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