Archives
Keywords
free Souslin tree Rainbow sets Erdos-Hajnal graphs PFA(S)[S] Cohen real Cardinal Invariants Kurepa Hypothesis Chromatic number Whitehead Problem P-Ideal Dichotomy Precaliber regressive Souslin tree strongly bounded groups Diamond full tree polarized partition relation Jonsson cardinal Coherent tree Sigma-Prikry Fast club Slim tree Absoluteness stationary reflection tensor product graph Subadditive reflection principles Open Access Iterated forcing weak diamond Filter reflection Poset specializable Souslin tree Lipschitz reduction C-sequence indecomposable ultrafilter Partition Relations Knaster Diamond for trees Constructible Universe super-Souslin tree ccc projective Boolean algebra unbounded function Rado's conjecture square diamond star Was Ulam right Subnormal ideal square principles Singular cardinals combinatorics Uniformization HOD Reflecting stationary set Selective Ultrafilter Distributive tree Rock n' Roll stationary hitting free Boolean algebra Large Cardinals Parameterized proxy principle Weakly compact cardinal Sakurai's Bell inequality b-scale Luzin set nonmeager set Generalized Clubs Universal Sequences Ramsey theory over partitions Souslin Tree Knaster and friends Foundations stick Almost Souslin Microscopic Approach Singular Density Dushnik-Miller Well-behaved magma xbox Local Club Condensation. Prevalent singular cardinals club_AD Generalized descriptive set theory Forcing Axioms Almost countably chromatic approachability ideal higher Baire space Hereditarily Lindelöf space Antichain Subtle tree property ZFC construction Fodor-type reflection GMA O-space AIM forcing Amenable C-sequence Reduced Power Greatly Mahlo S-Space Chang's conjecture Club Guessing Forcing Fat stationary set Subtle cardinal Vanishing levels Singular cofinality Ascent Path very good scale coloring number Square-Brackets Partition Relations transformations Sierpinski's onto mapping principle middle diamond Minimal Walks weak square Uniformly homogeneous positive partition relation Strongly Luzin set Hedetniemi's conjecture Strong coloring Axiom R Prikry-type forcing Hindman's Theorem Uniformly coherent 54G20 Martin's Axiom Small forcing Non-saturation PFA Closed coloring sap incompactness Nonspecial tree Shelah's Strong Hypothesis L-space Erdos Cardinal Analytic sets Mandelbrot set Postprocessing function Successor of Regular Cardinal Almost-disjoint family Cardinal function Ineffable cardinal Dowker space Diamond-sharp Ostaszewski square Successor of Singular Cardinal Aronszajn tree Commutative cancellative semigroups SNR Ulam matrix countably metacompact OCA
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
Comments Off on May the successor of a singular cardinal be Jonsson?
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, Partition Relations
Tagged Jonsson cardinal, Successor of Singular Cardinal
Comments Off on Perspectives on Set Theory, November 2023
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
2 Comments
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
1 Comment