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