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GMA Hereditarily Lindelöf space Reduced Power Jonsson cardinal Generalized descriptive set theory Amenable C-sequence Reflecting stationary set transformations Square-Brackets Partition Relations incompactness Rock n' Roll Subtle tree property positive partition relation Club Guessing free Boolean algebra Nonspecial tree Diamond-sharp Selective Ultrafilter Was Ulam right? Strongly compact cardinal Knaster Sakurai's Bell inequality Strongly Luzin set Ascent Path Rado's conjecture Martin's Axiom xbox square Constructible Universe very good scale Open Access Fast club C-sequence reflection principles S-Space Microscopic Approach stationary reflection Forcing Commutative cancellative semigroups Almost Souslin Singular cofinality Subnormal ideal Subtle cardinal Rainbow sets Ulam matrix Ineffable cardinal PFA(S)[S] projective Boolean algebra AIM forcing Weakly compact cardinal SNR Mandelbrot set Almost-disjoint family Sierpinski's onto mapping principle Prevalent singular cardinals Vanishing levels Sigma-Prikry indecomposable ultrafilter Forcing Axioms ZFC construction Countryman line Axiom R Closed coloring unbounded function Dushnik-Miller Lipschitz reduction Prikry-type forcing weak square Diamond weak diamond Singular cardinals combinatorics Kurepa Hypothesis Universal Sequences Uniformization Small forcing OCA Shelah's Strong Hypothesis Distributive tree super-Souslin tree Slim tree diamond star Poset Erdos-Hajnal graphs tensor product graph Iterated forcing Singular Density Coherent tree Souslin Tree Successor of Singular Cardinal Local Club Condensation. Postprocessing function Fodor-type reflection strongly bounded groups club_AD weak Kurepa tree regressive Souslin tree O-space Parameterized proxy principle Almost countably chromatic P-Ideal Dichotomy Foundations L-space middle diamond Antichain Whitehead Problem Erdos Cardinal stick Chromatic number Greatly Mahlo Non-saturation Partition Relations Hedetniemi's conjecture Knaster and friends full tree Respecting tree 54G20 nonmeager set Well-behaved magma sap Strong coloring Minimal Walks stationary hitting polarized partition relation Cohen real Dowker space Uniformly coherent higher Baire space Ostaszewski square b-scale Aronszajn tree Generalized Clubs specializable Souslin tree square principles countably metacompact Successor of Regular Cardinal Absoluteness Chang's conjecture Cardinal Invariants Intersection model Analytic sets Ramsey theory over partitions HOD coloring number Subadditive approachability ideal Diamond for trees Fat stationary set Hindman's Theorem Luzin set Commutative projection system PFA Uniformly homogeneous Filter reflection ccc free Souslin tree Precaliber Large Cardinals Cardinal function
Tag Archives: 03E02
A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Prikry-type forcing, 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
Posted in Groups, Publications
Tagged 03E02, 03E75, 20A15, 20E15, 20F06, Jonsson cardinal, Strong coloring, strongly bounded groups, Subadditive, ZFC construction
3 Comments
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right?
1 Comment
Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … 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
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
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, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E17, 03E35, GMA, Martin's Axiom, positive partition relation, Ramsey theory over partitions
1 Comment
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
Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
1 Comment
Rectangular square-bracket operation for successor of regular cardinals
Joint work with Stevo Todorcevic. Extended Abstract: Consider the coloring statement
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal
