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