Archives
Keywords
PFA Mandelbrot set ZFC construction Hereditarily Lindelöf space Diamond-sharp Prevalent singular cardinals Fast club Vanishing levels PFA(S)[S] Luzin set Cohen real reflection principles Open Access Chang's conjecture Subadditive b-scale Respecting tree middle diamond Antichain higher Baire space indecomposable filter incompactness Weakly compact cardinal specializable Souslin tree Successor of Singular Cardinal Uniformly coherent Coherent tree Ineffable cardinal Microscopic Approach Uniformization Precaliber Filter reflection Knaster and friends Prikry-type forcing Rock n' Roll Hindman's Theorem Was Ulam right? Almost-disjoint family Subnormal ideal square principles Whitehead Problem Fat stationary set Sierpinski's onto mapping principle Non-saturation Successor of Regular Cardinal polarized partition relation Generalized Clubs stationary reflection square Intersection model Subtle tree property Selective Ultrafilter HOD Singular cofinality Large Cardinals OCA Dowker space Parameterized proxy principle SNR Iterated forcing weak square nonmeager set Forcing Axioms Postprocessing function Jonsson cardinal Aronszajn tree Forcing Martin's Axiom Subtle cardinal Knaster Poset full tree Ramsey theory over partitions Partition Relations GMA ccc Analytic sets Foundations Ostaszewski square Singular cardinals combinatorics super-Souslin tree regressive Souslin tree Sigma-Prikry L-space C-sequence Singular Density projective Boolean algebra free Souslin tree Constructible Universe Commutative cancellative semigroups Greatly Mahlo Axiom R Amenable C-sequence Nonspecial tree Commutative projection system Diamond positive partition relation P-Ideal Dichotomy Well-behaved magma Diamond for trees countably metacompact Ulam matrix Ascent Path Generalized descriptive set theory Hedetniemi's conjecture Square-Brackets Partition Relations Sakurai's Bell inequality Cardinal function Countryman line Strongly compact cardinal transformations Almost countably chromatic coloring number club_AD Erdos Cardinal Lipschitz reduction Minimal Walks unbounded function Local Club Condensation. Distributive tree approachability ideal tensor product graph Universal Sequences Chromatic number Almost Souslin diamond star Fodor-type reflection Souslin Tree Reflecting stationary set Rado's conjecture Closed coloring very good scale Erdos-Hajnal graphs stationary hitting 54G20 AIM forcing Rainbow sets Slim tree free Boolean algebra weak diamond Uniformly homogeneous Kurepa Hypothesis Small forcing Strongly Luzin set Strong coloring S-Space O-space Club Guessing stick xbox Dushnik-Miller Cardinal Invariants weak Kurepa tree Reduced Power strongly bounded groups sap Absoluteness Shelah's Strong Hypothesis
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
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
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
3 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
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
