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