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positive partition relation polarized partition relation Forcing Axioms full tree Singular cofinality Ineffable cardinal Absoluteness Sierpinski's onto mapping principle xbox Microscopic Approach weak Kurepa tree stick Rock n' Roll Dowker space transformations Successor of Singular Cardinal Erdos-Hajnal graphs Kurepa Hypothesis O-space Selective Ultrafilter Analytic sets PFA Knaster and friends Dushnik-Miller Mandelbrot set Non-saturation Antichain Prevalent singular cardinals Successor of Regular Cardinal Foundations Square-Brackets Partition Relations club_AD Whitehead Problem Jonsson cardinal Distributive tree Aronszajn tree P-Ideal Dichotomy Local Club Condensation. Weakly compact cardinal Diamond S-Space Singular Density countably metacompact Large Cardinals Generalized descriptive set theory Cardinal function Singular cardinals combinatorics HOD weak diamond Partition Relations Rado's conjecture middle diamond Slim tree Nonspecial tree specializable Souslin tree Small forcing Commutative projection system nonmeager set Reduced Power Poset Hereditarily Lindelöf space Ulam matrix Ascent Path weak square Sigma-Prikry Erdos Cardinal Cardinal Invariants Strongly compact cardinal Ramsey theory over partitions Fast club Ostaszewski square sap Knaster Shelah's Strong Hypothesis Generalized Clubs Diamond for trees Constructible Universe Club Guessing Axiom R Martin's Axiom Prikry-type forcing square principles Uniformly coherent Uniformization Postprocessing function incompactness GMA Almost Souslin Chromatic number Countryman line Chang's conjecture approachability ideal tensor product graph SNR Sakurai's Bell inequality L-space Forcing Subadditive Almost countably chromatic ccc Filter reflection AIM forcing square OCA indecomposable ultrafilter super-Souslin tree Closed coloring unbounded function strongly bounded groups Precaliber Hindman's Theorem Amenable C-sequence Iterated forcing Cohen real very good scale free Boolean algebra Strong coloring free Souslin tree coloring number Souslin Tree Commutative cancellative semigroups diamond star C-sequence Diamond-sharp Strongly Luzin set Intersection model Reflecting stationary set Open Access Well-behaved magma Almost-disjoint family Coherent tree Respecting tree Minimal Walks 54G20 Vanishing levels projective Boolean algebra Parameterized proxy principle reflection principles Universal Sequences higher Baire space Luzin set Subtle cardinal Fat stationary set Rainbow sets ZFC construction regressive Souslin tree stationary reflection PFA(S)[S] Uniformly homogeneous stationary hitting Greatly Mahlo Subtle tree property b-scale Subnormal ideal Lipschitz reduction Fodor-type reflection Hedetniemi's conjecture Was Ulam right
Tag Archives: C-sequence
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Intersection models of generic extensions obtained from a commutative projection systems of notions of forcing has recently regained interest, especially in the study of descriptive set theory. Here, we show that … Continue reading
Posted in Compactness, Preprints
Tagged 03E05, 03E35, 03E55, Ascent Path, C-sequence, Commutative projection system, indecomposable ultrafilter, Intersection model, Strongly compact cardinal
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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 $Vspec(\kappa)$ 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
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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