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nonmeager set PFA diamond star C-sequence Cardinal function Prikry-type forcing Fodor-type reflection Whitehead Problem Kurepa Hypothesis Chromatic number OCA specializable Souslin tree Postprocessing function Knaster and friends higher Baire space Weakly compact cardinal Open Access stick Hereditarily Lindelöf space Diamond for trees Coherent tree Subadditive regressive Souslin tree Antichain Uniformization HOD Dowker space Diamond-sharp Closed coloring Singular cofinality Ostaszewski square coloring number Parameterized proxy principle Commutative cancellative semigroups O-space AIM forcing Erdos-Hajnal graphs Prevalent singular cardinals square Precaliber Commutative projection system club_AD Singular Density weak diamond Local Club Condensation. Mandelbrot set Rainbow sets ccc Reflecting stationary set unbounded function square principles Axiom R Singular cardinals combinatorics approachability ideal Countryman line weak square Distributive tree Aronszajn tree Rock n' Roll Generalized descriptive set theory Minimal Walks Dushnik-Miller incompactness Fat stationary set sap Poset Amenable C-sequence Intersection model Ineffable cardinal Lipschitz reduction Sakurai's Bell inequality free Boolean algebra Foundations Almost Souslin Successor of Singular Cardinal Forcing Ulam matrix Subtle cardinal Non-saturation Knaster Erdos Cardinal L-space weak Kurepa tree PFA(S)[S] free Souslin tree tensor product graph Martin's Axiom Filter reflection Sierpinski's onto mapping principle Cardinal Invariants Slim tree Universal Sequences Absoluteness b-scale Small forcing Constructible Universe Subnormal ideal Jonsson cardinal countably metacompact Generalized Clubs Shelah's Strong Hypothesis Strongly Luzin set Selective Ultrafilter Subtle tree property Souslin Tree S-Space positive partition relation polarized partition relation Hedetniemi's conjecture Strong coloring Large Cardinals Uniformly coherent full tree ZFC construction Square-Brackets Partition Relations Ramsey theory over partitions Club Guessing strongly bounded groups Successor of Regular Cardinal Respecting tree middle diamond GMA stationary reflection xbox Almost-disjoint family Microscopic Approach Uniformly homogeneous reflection principles Luzin set Partition Relations Chang's conjecture Strongly compact cardinal Fast club stationary hitting Was Ulam right Well-behaved magma Forcing Axioms Vanishing levels SNR Analytic sets Iterated forcing P-Ideal Dichotomy Almost countably chromatic 54G20 indecomposable ultrafilter Reduced Power Nonspecial tree Sigma-Prikry Ascent Path Diamond Rado's conjecture Cohen real Greatly Mahlo very good scale Hindman's Theorem super-Souslin tree transformations projective Boolean algebra
Tag Archives: Jonsson cardinal
May the successor of a singular cardinal be Jonsson?
Abstract: We collect necessary conditions for the successor of a singular cardinal to be Jónsson.
Posted in Open Problems, Singular Cardinals Combinatorics
Tagged Jonsson cardinal
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Perspectives on Set Theory, November 2023
I gave an invited talk at the Perspectives on Set Theory conference, November 2023. Talk Title: May the successor of a singular cardinal be Jónsson? Abstract: We’ll survey what’s known about the question in the title and collect ten open … Continue reading
Posted in Invited Talks, Open Problems
Tagged Jonsson cardinal, Successor of Singular Cardinal
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A Shelah group in ZFC
Joint work with Márk Poór. Abstract. In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group $G$ that moreover admits an integer $n$ satisfying … Continue reading
Posted in Groups, Preprints
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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