2 research outputs found
Moschovakis Extension of Represented Spaces
Given a represented space (in the sense of TTE theory), an appropriate
representation is constructed for the Moschovakis extension of its carrier
(with paying attention to the cases of effective topological spaces and
effective metric spaces). Some results are presented about TTE computability in
the represented space obtained in this way. For single-valued functions, we
prove, roughly speaking, the computability of any function which is absolutely
prime computable in some computable functions. A similar result holds for
multi-valued functions, but with an analog of absolute prime computability. The
formulation of this result makes use of the notion of computability in
iterative combinatory spaces - a notion studied by the author in other
publications.Comment: 21 pages. Intended for "Continuity, Computability, Constructivity:
From Logic to Algorithms" (postproceedings