10 found
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  1. Automatic Continuity of Group Homomorphisms.Christian Rosendal - 2009 - Bulletin of Symbolic Logic 15 (2):184-214.
    We survey various aspects of the problem of automatic continuity of homomorphisms between Polish groups.
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  2.  23
    Cofinal Families of Borel Equivalence Relations and Quasiorders.Christian Rosendal - 2005 - Journal of Symbolic Logic 70 (4):1325-1340.
    Families of Borel equivalence relations and quasiorders that are cofinal with respect to the Borel reducibility ordering, ≤B, are constructed. There is an analytic ideal on ω generating a complete analytic equivalence relation and any Borel equivalence relation reduces to one generated by a Borel ideal. Several Borel equivalence relations, among them Lipschitz isomorphism of compact metric spaces, are shown to be Kσ complete.
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  3.  50
    The Complexity of Continuous Embeddability Between Dendrites.Alberto Marcone & Christian Rosendal - 2004 - Journal of Symbolic Logic 69 (3):663-673.
    We show that the quasi-order of continuous embeddability between finitely branching dendrites (a natural class of fairly simple compacta) is $\Sigma_1^1$ -complete. We also show that embeddability between countable linear orders with infinitely many colors is $\Sigma_1^1$ -complete.
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  4.  25
    Finitely Approximable Groups and Actions Part I: The Ribes—Zaluesskiĭ Property.Christian Rosendal - 2011 - Journal of Symbolic Logic 76 (4):1297-1306.
    We investigate extensions of S. Solecki's theorem on closing off finite partial isometries of metric spaces [11] and obtain the following exact equivalence: any action of a discrete group Γ by isometries of a metric space is finitely approximable if and only if any product of finitely generated subgroups of Γ is closed in the profinite topology on Γ.
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  5.  22
    Completely Metrisable Groups Acting on Trees.Christian Rosendal - 2011 - Journal of Symbolic Logic 76 (3):1005 - 1022.
    We consider actions of completely metrisable groups on simplicial trees in the context of the Bass—Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild conditions on a completely metrisable group G, namely, that the set of elements generating a non-discrete or finite subgroup is somewhere dense, we show that in any decomposition as a free product with amalgamation, G = A * C B, the amalgamated groups A, B and C (...)
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  6.  17
    Finitely Approximable Groups and Actions Part II: Generic Representations.Christian Rosendal - 2011 - Journal of Symbolic Logic 76 (4):1307-1321.
    Given a finitely generated group Γ, we study the space Isom(Γ, ℚ) of all actions of Γ by isometries of the rational Urysohn metric space ℚ, where Isom(Γ, ℚ) is equipped with the topology it inherits seen as a closed subset of Isom(ℚ) Γ . When Γ is the free group n on n generators this space is just Isom(ℚ) n , but is in general significantly more complicated. We prove that when Γ is finitely generated Abelian there is (...)
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  7.  8
    Compact Metrizable Structures and Classification Problems.Christian Rosendal & Joseph Zielinski - 2018 - Journal of Symbolic Logic 83 (1):165-186.
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  8.  21
    Universally Measurable Subgroups of Countable Index.Christian Rosendal - 2010 - Journal of Symbolic Logic 75 (3):1081-1086.
    It is proved that any countable index, universally measurable subgroup of a Polish group is open. By consequence, any universally measurable homomorphism from a Polish group into the infinite symmetric group S ∞ is continuous. It is also shown that a universally measurable homomorphism from a Polish group into a second countable, locally compact group is necessarily continuous.
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  9. Marriott Wardman Park Hotel, Washington, DC January 7–8, 2009.Barbara F. Csima, Inessa Epstein, Rahim Moosa, Christian Rosendal, Jouko Väänänen & Ali Enayat - 2009 - Bulletin of Symbolic Logic 15 (2).
     
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  10.  6
    Superstability and Categoricity in Abstract Elementary Classes, Carnegie Mellon University, USA, 2017. Supervised by Rami Grossberg.Christian Rosendal & Sebastien Vasey - 2018 - Bulletin of Symbolic Logic 24 (2):192-194.
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