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