### Sigma^0_alpha - Admissible Representations (Extended Abstract)

Matthew De Brecht & Akihiro Yamamoto
We investigate a hierarchy of representations of topological spaces by measurable functions that extends the traditional notion of admissible representations common to computable analysis. Specific instances of these representations already occur in the literature (for example, the naive Cauchy representation of the reals and the jump'' of a representation), and have been used in investigating the computational properties of discontinuous functions. Our main contribution is the integration of a recently developing descriptive set theory for...