Results 21 to 30 of about 71 (54)

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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Complexity of finite Borel asymptotic dimension

Forum of Mathematics, Sigma
We 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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Hjorth’s Reflection Argument

Forum of Mathematics, Sigma
In [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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Tree-like graphings, wallings, and median graphings of equivalence relations

Forum of Mathematics, Sigma
We prove several results showing that every locally finite Borel graph whose large-scale geometry is ‘tree-like’ induces a treeable equivalence relation.
Ruiyuan Chen, Antoine Poulin, Ran Tao, Anush Tserunyan   +3 more
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Measurable Vizing’s theorem

Forum of Mathematics, Sigma
We prove a full measurable version of Vizing’s theorem for bounded degree Borel graphs, that is, we show that every Borel graph $\mathcal {G}$ of degree uniformly bounded by $\Delta \in \mathbb {N}$ defined on a standard probability space
Jan Grebík
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Structural, point-free, non-Hausdorff topological realization of Borel groupoid actions

Forum of Mathematics, Sigma
We extend the Becker–Kechris topological realization and change-of-topology theorems for Polish group actions in several directions. For Polish group actions, we prove a single result that implies the original Becker–Kechris theorems, as well as Sami’s ...
Ruiyuan Chen
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Local entropy theory and descriptive complexity

Forum of Mathematics, Sigma
We investigate local entropy theory, particularly the property of having completely positive entropy (CPE), from a descriptive set-theoretic point of view. We aim to determine the descriptive complexity of different families of dynamical systems with CPE.
Felipe García-Ramos, Udayan B. Darji
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The definable content of homological invariants II: Čech cohomology and homotopy classification

Forum of Mathematics, Pi
This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebraic topology.
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos   +2 more
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Analytic digraphs of uncountable Borel chromatic number under injective definable homomorphism

, 2018
We study the analytic digraphs of uncountable Borel chromatic number on Polish spaces, and compare them with the notion of injective Borel homomorphism. We provide some minimal digraphs incomparable with G 0.
Zeleny, Miroslav, Lecomte, Dominique
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On Strong Measure Zero Subsets of ...

, 1997
This paper answers three questions posed in [1]. Theorem 2.7 The family of strong measure zero subsets of ! 1 2 is 2 @ 1 -additive under GMA and CH. Theorem 3.1 The generalized Borel conjecture is false in ! 1 2 assuming ZFC+CH.
Aapo Halko, Saharon Shelah
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