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unbounded function Mandelbrot set Ulam matrix indecomposable filter higher Baire space reflection principles nonmeager set Small forcing Nonspecial tree Cardinal function ZFC construction Absoluteness Closed coloring tensor product graph Large Cardinals Foundations Rado's conjecture Subnormal ideal Jonsson cardinal Aronszajn tree C-sequence Uniformly coherent Diamond Poset Forcing Axioms Greatly Mahlo Iterated forcing Intersection model Filter reflection PFA(S)[S] xbox Subadditive Luzin set square Antichain Constructible Universe Subtle cardinal Axiom R Slim tree Prikry-type forcing P-Ideal Dichotomy Knaster Monotonically far Strongly Luzin set Universal Sequences 54G20 weak Kurepa tree middle diamond Sakurai's Bell inequality OCA Ramsey theory over partitions Well-behaved magma Weakly compact cardinal weak square Vanishing levels HOD specializable Souslin tree regressive Souslin tree Respecting tree Diamond for trees Diamond-sharp sap b-scale polarized partition relation free Souslin tree Cardinal Invariants Lipschitz reduction Minimal Walks Commutative cancellative semigroups Hedetniemi's conjecture Forcing Microscopic Approach ccc Countryman line Commutative projection system Amenable C-sequence strongly bounded groups Hindman's Theorem weak diamond Dushnik-Miller O-space Successor of Singular Cardinal S-Space Generalized descriptive set theory Chromatic number Shelah's Strong Hypothesis Distributive tree full tree Prevalent singular cardinals Rock n' Roll Postprocessing function square principles Whitehead Problem countably metacompact Analytic sets Erdos Cardinal Uniformly homogeneous Erdos-Hajnal graphs Knaster and friends Fodor-type reflection super-Souslin tree PFA free Boolean algebra Uniformization Parameterized proxy principle Selective Ultrafilter Hereditarily Lindelöf space stick Reduced Power club_AD coloring number Successor of Regular Cardinal Strongly compact cardinal Open Access Souslin Tree Almost Souslin positive partition relation Precaliber Singular Density Fast club Strong coloring Was Ulam right? SNR GMA Fat stationary set Singular cofinality Ascent Path Local Club Condensation. diamond star Non-saturation stationary hitting Almost countably chromatic Ineffable cardinal Club Guessing Kurepa Hypothesis transformations Chang's conjecture Subtle tree property Martin's Axiom Rainbow sets stationary reflection projective Boolean algebra L-space AIM forcing Ostaszewski square Sierpinski's onto mapping principle incompactness Square-Brackets Partition Relations Partition Relations Cohen real Reflecting stationary set Sigma-Prikry approachability ideal Generalized Clubs Almost-disjoint family Dowker space Singular cardinals combinatorics Coherent tree Entangled family very good scale
Tag Archives: 03E55
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 filter, Intersection model, Strongly compact cardinal
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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
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
Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is
Posted in Compactness, Publications
Tagged 03E35, 03E55, 03E65, 03E75, 03G05, 06E05, Axiom R, Fodor-type reflection, free Boolean algebra, projective Boolean algebra, Shelah's Strong Hypothesis, stationary reflection
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On the consistency strength of the Milner-Sauer conjecture
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset
