Samuel Coskey
Infinite time decidable equivalence relation theory.
Tue, 10/27/2009 - 16:01 — SomNambulAuthors: Samuel Coskey, Joel David Hamkins
Subjects: Logic
AbstractWe introduce an analog of the theory of Borel equivalence relations in which
we study equivalence relations that are decidable by an infinite time Turing
machine. The Borel reductions are replaced by the more general class of
infinite time computable functions. Many basic aspects of the classical theory
remain intact, with the added bonus that it becomes sensible to study some
special equivalence relations whose complexity is beyond Borel or even
analytic.Borel reductions of profinite actions of SL(n,Z).
Fri, 09/04/2009 - 12:10 — SomNambulAuthors: Samuel Coskey
Subjects: Logic
AbstractGreg Hjorth and Simon Thomas proved that the classification problem for
torsion-free abelian groups of finite rank \emph{strictly increases} in
complexity with the rank. Subsequently, Thomas proved that the complexity of
the classification problems for $p$-local torsion-free abelian groups of fixed
rank $n$ are \emph{pairwise incomparable} as $p$ varies.
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