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Connecting topological dimension theory and recursion theory

Thursday 27th August 2015 - 13:30 to 14:00
INI Seminar Room 2
We introduce the point degree spectrum of a represented spaces as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees, and so on. The point degree spectrum connects descriptive set theory, topological dimension theory and computability theory. Through this new connection, for instance, we construct a family of continuum many infinite dimensional Cantor manifolds possessing Haver's property C whose Borel structures at an arbitrary finite rank are mutually non-isomorphic, which strengthen various theorems in infinite dimensional topology such as Roman Pol's solution to Pavel Alexandrov's old problem.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons