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Reflecting stationary set Commutative projection system Subtle cardinal Ulam matrix Cardinal function Microscopic Approach Uniformly homogeneous Strongly Luzin set PFA(S)[S] Almost countably chromatic Jonsson cardinal Uniformly coherent Large Cardinals Cohen real Sigma-Prikry diamond star Iterated forcing Weakly compact cardinal SNR Almost Souslin Aronszajn tree polarized partition relation Strongly compact cardinal Rainbow sets coloring number Diamond very good scale full tree stationary hitting Fast club Singular Density Postprocessing function GMA P-Ideal Dichotomy Vanishing levels tensor product graph square principles countably metacompact Rado's conjecture Uniformization Nonspecial tree Hindman's Theorem Diamond for trees Singular cardinals combinatorics Hedetniemi's conjecture Fodor-type reflection AIM forcing Universal Sequences Analytic sets Prevalent singular cardinals Well-behaved magma xbox Lipschitz reduction Shelah's Strong Hypothesis Mandelbrot set Souslin Tree Amenable C-sequence transformations Filter reflection Commutative cancellative semigroups Countryman line weak diamond Forcing Strong coloring super-Souslin tree Ascent Path Forcing Axioms Cardinal Invariants free Souslin tree weak Kurepa tree Sakurai's Bell inequality HOD Dushnik-Miller Constructible Universe Successor of Singular Cardinal Non-saturation Antichain Ineffable cardinal Kurepa Hypothesis weak square b-scale Chromatic number Whitehead Problem club_AD middle diamond Singular cofinality Subtle tree property Knaster ccc Small forcing Was Ulam right? Luzin set Generalized Clubs Absoluteness Subnormal ideal Local Club Condensation. Parameterized proxy principle O-space Distributive tree Generalized descriptive set theory Erdos Cardinal Precaliber Chang's conjecture Ostaszewski square OCA Diamond-sharp Subadditive S-Space Hereditarily Lindelöf space indecomposable ultrafilter Respecting tree Dowker space Club Guessing Sierpinski's onto mapping principle Open Access C-sequence incompactness Partition Relations Almost-disjoint family Prikry-type forcing Martin's Axiom Poset Axiom R PFA Foundations regressive Souslin tree square stick specializable Souslin tree reflection principles Fat stationary set Closed coloring strongly bounded groups stationary reflection Intersection model Rock n' Roll unbounded function L-space Knaster and friends Reduced Power 54G20 Successor of Regular Cardinal free Boolean algebra Minimal Walks Ramsey theory over partitions Greatly Mahlo Erdos-Hajnal graphs sap Coherent tree higher Baire space ZFC construction projective Boolean algebra Square-Brackets Partition Relations nonmeager set Slim tree approachability ideal positive partition relation Selective Ultrafilter
Category Archives: Partition Relations
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
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, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E17, 03E35, GMA, Martin's Axiom, positive partition relation, Ramsey theory over partitions
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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
Knaster and friends I: Closed colorings and precalibers
Joint work with Chris Lambie-Hanson. Abstract. The productivity of the
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
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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Chain conditions of products, and weakly compact cardinals
Abstract. The history of productivity of the
Posted in Partition Relations, Publications
Tagged Aronszajn tree, ccc, Fat stationary set, Minimal Walks, square, Weakly compact cardinal
2 Comments
Complicated colorings
Abstract. If
Posted in Partition Relations, Publications
Tagged Minimal Walks, Open Access, Square-Brackets Partition Relations
2 Comments
Rectangular square-bracket operation for successor of regular cardinals
Joint work with Stevo Todorcevic. Extended Abstract: Consider the coloring statement
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal
