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William Chan
University of Manchester
  1.  19
    Ordinal Definability and Combinatorics of Equivalence Relations.William Chan - 2019 - Journal of Mathematical Logic 19 (2):1950009.
    Assume [Formula: see text]. Let [Formula: see text] be a [Formula: see text] equivalence relation coded in [Formula: see text]. [Formula: see text] has an ordinal definable equivalence class without any ordinal definable elements if and only if [Formula: see text] is unpinned. [Formula: see text] proves [Formula: see text]-class section uniformization when [Formula: see text] is a [Formula: see text] equivalence relation on [Formula: see text] which is pinned in every transitive model of [Formula: see text] containing the real (...)
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  2.  21
    The Countable Admissible Ordinal Equivalence Relation.William Chan - 2017 - Annals of Pure and Applied Logic 168 (6):1224-1246.
  3.  1
    Bounds on Scott Ranks of Some Polish Metric Spaces.William Chan - 2020 - Journal of Mathematical Logic 21 (1):2150001.
    If [Formula: see text] is a proper Polish metric space and [Formula: see text] is any countable dense submetric space of [Formula: see text], then the Scott rank of [Formula: see text] in the natural first-order language of metric spaces is countable and in fact at most [Formula: see text], where [Formula: see text] is the Church–Kleene ordinal of [Formula: see text] which is the least ordinal with no presentation on [Formula: see text] computable from [Formula: see text]. If [Formula: (...)
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    Cardinality of Wellordered Disjoint Unions of Quotients of Smooth Equivalence Relations.William Chan & Stephen Jackson - 2021 - Annals of Pure and Applied Logic 172 (8):102988.
  5.  7
    Equivalence Relations Which Are Borel Somewhere.William Chan - 2017 - Journal of Symbolic Logic 82 (3):893-930.
    The following will be shown: Let I be a σ-ideal on a Polish space X so that the associated forcing of I+${\bf{\Delta }}_1^1$ sets ordered by ⊆ is a proper forcing. Let E be a ${\bf{\Sigma }}_1^1$ or a ${\bf{\Pi }}_1^1$ equivalence relation on X with all equivalence classes ${\bf{\Delta }}_1^1$. If for all $z \in {H_{{{\left}^ + }}}$, z♯ exists, then there exists an I+${\bf{\Delta }}_1^1$ set C ⊆ X such that E ↾ C is a ${\bf{\Delta }}_1^1$ equivalence (...)
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