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