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