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