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Kurepa Hypothesis Well-behaved magma Iterated forcing Knaster and friends SNR countably metacompact Jonsson cardinal approachability ideal Respecting tree Analytic sets Sakurai's Bell inequality square Ascent Path Slim tree Reduced Power weak diamond Whitehead Problem S-Space PFA Ulam matrix Axiom R Strong coloring Foundations Strongly Luzin set diamond star Generalized Clubs Reflecting stationary set Filter reflection ZFC construction Prikry-type forcing Cohen real AIM forcing Partition Relations stick Greatly Mahlo Rock n' Roll weak square C-sequence coloring number stationary hitting Microscopic Approach ccc square principles Amenable C-sequence stationary reflection Distributive tree Diamond for trees Commutative projection system Ostaszewski square Strongly compact cardinal Universal Sequences HOD Uniformly homogeneous P-Ideal Dichotomy Shelah's Strong Hypothesis Cardinal Invariants Cardinal function Countryman line Rado's conjecture Successor of Singular Cardinal Rainbow sets incompactness Mandelbrot set very good scale full tree Sigma-Prikry Open Access polarized partition relation PFA(S)[S] Fast club L-space xbox Dushnik-Miller transformations Dowker space Subtle tree property Erdos Cardinal weak Kurepa tree Aronszajn tree free Souslin tree club_AD regressive Souslin tree Closed coloring Club Guessing reflection principles nonmeager set Hindman's Theorem OCA Intersection model Fat stationary set Chang's conjecture Was Ulam right Almost countably chromatic Selective Ultrafilter Coherent tree Fodor-type reflection Postprocessing function Small forcing GMA specializable Souslin tree Ramsey theory over partitions Poset Souslin Tree Prevalent singular cardinals O-space super-Souslin tree Square-Brackets Partition Relations Luzin set Hedetniemi's conjecture Singular cofinality Generalized descriptive set theory Erdos-Hajnal graphs Singular Density Almost-disjoint family Weakly compact cardinal Uniformization Almost Souslin Minimal Walks positive partition relation Forcing Axioms 54G20 Commutative cancellative semigroups Diamond Singular cardinals combinatorics Subadditive Ineffable cardinal Antichain tensor product graph b-scale Uniformly coherent Nonspecial tree Hereditarily Lindelöf space free Boolean algebra Local Club Condensation. Constructible Universe Subtle cardinal Forcing Diamond-sharp Non-saturation indecomposable ultrafilter sap Lipschitz reduction Large Cardinals Parameterized proxy principle middle diamond projective Boolean algebra Chromatic number Sierpinski's onto mapping principle Martin's Axiom Precaliber Knaster strongly bounded groups higher Baire space unbounded function Successor of Regular Cardinal Subnormal ideal Vanishing levels Absoluteness
Tag Archives: Strong coloring
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. It is proved that if there is an $\aleph_2$-Aronszajn line, then there is one that does not contain an $\aleph_2$-Countryman line. This solves a problem of Moore and stands in a sharp contrast with … 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, Preprints
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, 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
