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