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