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