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Dushnik-Miller Shelah's Strong Hypothesis Generalized descriptive set theory HOD regressive Souslin tree ZFC construction Weakly compact cardinal Greatly Mahlo Nonspecial tree middle diamond Hedetniemi's conjecture Whitehead Problem diamond star ccc approachability ideal Distributive tree b-scale Successor of Singular Cardinal Axiom R Partition relations for trees Subnormal ideal Hindman's Theorem stationary hitting perfectly normal Generalized Clubs Hereditarily Lindelöf space OCA Well-behaved magma indecomposable filter Singular cofinality Small forcing GMA Knaster nonmeager set Microscopic Approach square principles Large Cardinals Interval topology on trees Ostaszewski square SNR Coherent tree Ineffable cardinal super-Souslin tree Rainbow sets Forcing Axioms Dowker space Constructible Universe Fodor-type reflection incompactness Was Ulam right? unbounded function Ulam matrix Forcing with side conditions club_AD Singular Density Jonsson cardinal Fast club Almost-disjoint family Almost countably chromatic Monotonically far strongly bounded groups Strong coloring Closed coloring square free Boolean algebra reflection principles Souslin Tree Knaster and friends Square-Brackets Partition Relations Poset 54G20 Iterated forcing PFA Uniformly coherent positive partition relation Cohen real Antichain full tree Singular cardinals combinatorics projective Boolean algebra Commutative projection system Rock n' Roll weak Kurepa tree Vanishing levels specializable Souslin tree Precaliber Uniformization Parameterized proxy principle Ramsey theory over partitions Open Access Sakurai's Bell inequality Rado's conjecture Erdos Cardinal stick Fat stationary set Diamond for trees Foundations Lipschitz reduction Ascent Path weak diamond sap very good scale Club Guessing weak square Respecting tree xbox Luzin set Erdos-Hajnal graphs Sierpinski's onto mapping principle Chang's conjecture P-Ideal Dichotomy Strongly Luzin set coloring number Commutative cancellative semigroups Intersection model Prikry-type forcing Slim tree Selective Ultrafilter Cardinal Invariants AIM forcing free Souslin tree Analytic sets Strongly compact cardinal Prevalent singular cardinals Forcing Successor of Regular Cardinal Ascending path Countryman line L-space Partition Relations Filter reflection Chromatic number Reduced Power Diamond Diamond-sharp Minimal Walks polarized partition relation Kurepa Hypothesis Aronszajn tree C-sequence Martin's Axiom Subtle tree property Postprocessing function higher Baire space Subadditive Entangled linear order stationary reflection Subtle cardinal O-space Amenable C-sequence Non-saturation Absoluteness tensor product graph transformations countably metacompact Universal Sequences Sigma-Prikry Uniformly homogeneous S-Space PFA(S)[S] Almost Souslin Local Club Condensation. Reflecting stationary set Mandelbrot set Cardinal function
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 $G$ that moreover admits an integer $n$ satisfying … Continue reading
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Open Access, 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, Entangled linear order, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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Hedetniemi’s conjecture for uncountable graphs
Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal $\kappa$, there exist graphs $\mathcal G$ and $\mathcal H$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal G\times\mathcal H$ is countably chromatic. … 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 $\aleph _2$-projective. Previously it was known that this … Continue reading
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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