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