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Benjamin Miller
University of Illinois, Urbana-Champaign
  1.  39
    The Graph-Theoretic Approach to Descriptive Set Theory.Benjamin D. Miller - 2012 - Bulletin of Symbolic Logic 18 (4):554-575.
    We sketch the ideas behind the use of chromatic numbers in establishing descriptive set-theoretic dichotomy theorems.
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  2.  10
    An Embedding Theorem Of.Itay Kaplan & Benjamin D. Miller - 2014 - Journal of Mathematical Logic 14 (2):1450010.
    We provide a new criterion for embedding.
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  3.  2
    On the Existence of Small Antichains for Definable Quasi-Orders.Raphael Carroy, Benjamin D. Miller & Zoltan Vidnyanszky - forthcoming - Journal of Mathematical Logic.
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  4.  34
    Dichotomy Theorems for Countably Infinite Dimensional Analytic Hypergraphs.Benjamin D. Miller - 2011 - Annals of Pure and Applied Logic 162 (7):561-565.
    We give classical proofs, strengthenings, and generalizations of Lecomte’s characterizations of analytic ω-dimensional hypergraphs with countable Borel chromatic number.
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  5.  21
    Basis Theorems for Non-Potentially Closed Sets and Graphs of Uncountable Borel Chromatic Number.Dominique Lecomte & Benjamin D. Miller - 2008 - Journal of Mathematical Logic 8 (2):121-162.
    We show that there is an antichain basis for neither the class of non-potentially closed Borel subsets of the plane under Borel rectangular reducibility nor the class of analytic graphs of uncountable Borel chromatic number under Borel reducibility.
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  6.  16
    Measurable Chromatic Numbers.Benjamin D. Miller - 2008 - Journal of Symbolic Logic 73 (4):1139-1157.
    We show that if add(null) = c, then the globally Baire and universally measurable chromatic numbers of the graph of any Borel function on a Polish space are equal and at most three. In particular, this holds for the graph of the unilateral shift on [N]N, although its Borel chromatic number is N₀. We also show that if add(null) = c, then the universally measurable chromatic number of every treeing of a measure amenable equivalence relation is at most three. In (...)
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  7.  3
    On the Existence of Large Antichains for Definable Quasi-Orders.Benjamin D. Miller & Zoltán Vidnyánszky - 2020 - Journal of Symbolic Logic 85 (1):103-108.
    We simultaneously generalize Silver’s perfect set theorem for co-analytic equivalence relations and Harrington-Marker-Shelah’s Dilworth-style perfect set theorem for Borel quasi-orders, establish the analogous theorem at the next definable cardinal, and give further generalizations under weaker definability conditions.
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  8.  10
    Measurable Perfect Matchings for Acyclic Locally Countable Borel Graphs.Clinton T. Conley & Benjamin D. Miller - 2017 - Journal of Symbolic Logic 82 (1):258-271.
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