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Filter reflection Erdos Cardinal Closed coloring Forcing Axioms Lipschitz reduction Entangled linear order Reflecting stationary set Sigma-Prikry club_AD Diamond-sharp strongly bounded groups regressive Souslin tree Amenable C-sequence positive partition relation Iterated forcing stationary hitting Ostaszewski square Analytic sets Mandelbrot set Square-Brackets Partition Relations Coherent tree approachability ideal Uniformly homogeneous Almost Souslin Interval topology on trees Prikry-type forcing Subnormal ideal Postprocessing function Absoluteness square principles Uniformly coherent Successor of Singular Cardinal Fast club Dowker space Souslin Tree S-Space Monotonically far Chang's conjecture Ascending path Fat stationary set Forcing Almost countably chromatic Greatly Mahlo very good scale Small forcing Commutative projection system Martin's Axiom Constructible Universe Knaster O-space Singular cardinals combinatorics Large Cardinals Strong coloring transformations free Boolean algebra nonmeager set Cardinal Invariants Luzin set Rock n' Roll Subtle cardinal Shelah's Strong Hypothesis higher Baire space unbounded function SNR free Souslin tree stationary reflection incompactness specializable Souslin tree full tree Intersection model GMA Precaliber Sierpinski's onto mapping principle ZFC construction Rado's conjecture weak Kurepa tree projective Boolean algebra Non-saturation Cardinal function Aronszajn tree Subtle tree property Strongly Luzin set Commutative cancellative semigroups Generalized Clubs square Hindman's Theorem polarized partition relation HOD Parameterized proxy principle Selective Ultrafilter Axiom R Chromatic number Microscopic Approach Prevalent singular cardinals middle diamond diamond star Almost-disjoint family Knaster and friends sap Erdos-Hajnal graphs Was Ulam right? Reduced Power Slim tree Weakly compact cardinal Vanishing levels Well-behaved magma Ramsey theory over partitions Strongly compact cardinal Jonsson cardinal Foundations Generalized descriptive set theory Partition relations for trees Cohen real Respecting tree Rainbow sets Distributive tree stick Minimal Walks L-space Successor of Regular Cardinal Local Club Condensation. Partition Relations perfectly normal Poset Ascent Path Forcing with side conditions C-sequence PFA(S)[S] Fodor-type reflection weak diamond PFA Diamond Uniformization b-scale Kurepa Hypothesis Open Access Diamond for trees Club Guessing super-Souslin tree Hereditarily Lindelöf space P-Ideal Dichotomy Ineffable cardinal Singular cofinality 54G20 Ulam matrix weak square reflection principles Singular Density Subadditive Sakurai's Bell inequality ccc countably metacompact Antichain xbox Whitehead Problem Hedetniemi's conjecture Baumgartner's square AIM forcing Universal Sequences indecomposable filter OCA coloring number tensor product graph Nonspecial tree Dushnik-Miller Countryman line
Tag Archives: Strong coloring
Conference in honor of Saharon Shelah’s 80th birthday
I gave an invited talk at the conference in honor of Shelah’s 80th birthday, July 2025. Talk Title: Marginalia to [Sh:365] Abstract: Solovay famously proved that every stationary subset of a regular uncountable cardinal kappa may be decomposed into kappa … Continue reading
Posted in Invited Talks
Tagged Greatly Mahlo, Strong coloring, Was Ulam right?
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Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Posted in Basis problems, Partition Relations, Preprints
Tagged Aronszajn tree, Ascending path, Club Guessing, Countryman line, Entangled linear order, Minimal Walks, Monotonically far, Partition relations for trees, Strong coloring, Subtle tree property, Vanishing levels, ZFC construction
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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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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
