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Singular cofinality Square-Brackets Partition Relations Diamond-sharp Postprocessing function Vanishing levels Was Ulam right square diamond star Large Cardinals nonmeager set weak Kurepa tree Shelah's Strong Hypothesis free Boolean algebra indecomposable ultrafilter Commutative cancellative semigroups weak diamond S-Space Rock n' Roll club_AD Microscopic Approach Aronszajn tree Ascent Path Hedetniemi's conjecture incompactness Chromatic number positive partition relation Fodor-type reflection Rainbow sets Lipschitz reduction Almost-disjoint family Strong coloring regressive Souslin tree Sigma-Prikry stationary hitting Sierpinski's onto mapping principle Selective Ultrafilter Reflecting stationary set polarized partition relation Erdos Cardinal Parameterized proxy principle Hereditarily Lindelöf space Subadditive Singular cardinals combinatorics Non-saturation Uniformization Jonsson cardinal Dushnik-Miller xbox Subtle tree property AIM forcing Club Guessing tensor product graph Strongly Luzin set Whitehead Problem Diamond PFA(S)[S] Greatly Mahlo very good scale Dowker space specializable Souslin tree free Souslin tree Cardinal function Almost Souslin Iterated forcing projective Boolean algebra Partition Relations weak square Mandelbrot set Successor of Singular Cardinal approachability ideal HOD Well-behaved magma Knaster and friends Chang's conjecture Forcing Souslin Tree Uniformly homogeneous Uniformly coherent SNR Analytic sets Erdos-Hajnal graphs Luzin set C-sequence Absoluteness Hindman's Theorem Antichain Local Club Condensation. Singular Density Ramsey theory over partitions 54G20 Sakurai's Bell inequality Ostaszewski square stationary reflection Cardinal Invariants countably metacompact b-scale Ineffable cardinal strongly bounded groups Minimal Walks Subtle cardinal Open Access Diamond for trees stick Constructible Universe Weakly compact cardinal L-space Small forcing Precaliber coloring number transformations super-Souslin tree ZFC construction Axiom R Prevalent singular cardinals sap Successor of Regular Cardinal Fat stationary set ccc Kurepa Hypothesis Slim tree Ulam matrix Closed coloring full tree Generalized Clubs Knaster Nonspecial tree GMA Distributive tree OCA P-Ideal Dichotomy middle diamond Universal Sequences Fast club O-space Filter reflection Amenable C-sequence unbounded function reflection principles Generalized descriptive set theory Reduced Power Foundations Coherent tree Cohen real Subnormal ideal Forcing Axioms higher Baire space Prikry-type forcing PFA Almost countably chromatic Rado's conjecture Poset square principles Martin's Axiom
Tag Archives: Strong coloring
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, Preprints
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
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Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems
Joint work with Menachem Kojman and Juris Steprāns. Abstract. In this series of papers, we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in … Continue reading
Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Joint work with Menachem Kojman and Juris Steprāns. Abstract. The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of … Continue reading
Transformations of the transfinite plane
Joint work with Jing Zhang. Abstract. We study the existence of transformations of the transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for uncountable cardinals. To exemplify: we prove that for every … Continue reading
