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