Results 11 to 20 of about 52 (52)
ANALYTIC EQUIVALENCE RELATIONS SATISFYING HYPERARITHMETIC-IS-RECURSIVE
Forum of Mathematics, Sigma, 2015 We prove, in $\text{ZF}+\boldsymbol{{\it\Sigma}}_{2}^{1}$-determinacy, that, for any analytic equivalence relation $E$, the following three statements are equivalent: (1) $E$ does not have perfectly many classes, (2) $E$ satisfies hyperarithmetic-is ...
ANTONIO MONTALBÁN
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CONTINUITY OF UNIVERSALLY MEASURABLE HOMOMORPHISMS
Forum of Mathematics, Pi, 2019 Answering a longstanding problem originating in Christensen’s seminal work on Haar null sets [Math. Scand. 28 (1971), 124–128; Israel J. Math. 13 (1972), 255–260; Topology and Borel Structure.
CHRISTIAN ROSENDAL
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BROOKS’ THEOREM FOR MEASURABLE COLORINGS
Forum of Mathematics, Sigma, 2016 We generalize Brooks’ theorem to show that if $G$ is a Borel graph on a standard Borel space $
CLINTON T. CONLEY +2 more
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Hyperfiniteness of boundary actions of acylindrically hyperbolic groups
Forum of Mathematics, SigmaWe prove that, for any countable acylindrically hyperbolic group G, there exists a generating set S of G such that the corresponding Cayley graph $\Gamma (G,S)$ is hyperbolic, $|\partial \Gamma (G,S)|>2$ , the natural action of G on ...
Koichi Oyakawa
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KŐNIG’S LINE COLORING AND VIZING’S THEOREMS FOR GRAPHINGS
Forum of Mathematics, Sigma, 2016 The classical theorem of Vizing states that every graph of maximum degree $d$ admits an edge coloring with at most
ENDRE CSÓKA +2 more
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Adequate Compacta which are Gul’ko or Talagrand [PDF]
, 2003 2000 Mathematics Subject Classification: 54H05, 03E15, 46B26We answer positively a question raised by S. Argyros: Given any coanalytic, nonalytic subset Σ′ of the irrationals, we construct, in Mercourakis space c1(Σ′), an adequate compact which is Gul’ko
Fabian, Marián, Čížek, Petr
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A model of the Axiom of Determinacy in which every set of reals is universally Baire
Forum of Mathematics, SigmaThe consistency of the theory $\mathsf {ZF} + \mathsf {AD}_{\mathbb {R}} + {}$ ‘every set of reals is universally Baire’ is proved relative to $\mathsf {ZFC} + {}$ ‘there is a cardinal that is a limit of Woodin cardinals and of strong ...
Paul B. Larson +2 more
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Forum of Mathematics, PiWe introduce new types of examples of bounded degree acyclic Borel graphs and study their combinatorial properties in the context of descriptive combinatorics, using a generalization of the determinacy method of Marks [Mar16].
Sebastian Brandt +5 more
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Complexity of finite Borel asymptotic dimension
Forum of Mathematics, SigmaWe show that the set of locally finite Borel graphs with finite Borel asymptotic dimension is $\boldsymbol {\Sigma }^1_2$ -complete. The result is based on a combinatorial characterization of finite Borel asymptotic dimension for graphs generated ...
Jan Grebík, Cecelia Higgins
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Forum of Mathematics, SigmaIn [7], Hjorth, assuming $\mathsf {{AD+ZF+DC}}$ , showed that there is no sequence of length $\omega _2$ consisting of distinct $\boldsymbol {\Sigma }^1_2$ -sets. We show that the same theory implies that for $n\geq 0$ , there is
Grigor Sargsyan
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