A. Bauer. Topology and computability. Thesis Proposal, April 1998.  Home/Search   Document Details and Download   Summary   Related Articles

....: T ]U . By employing this modal logic, one will be able to reason about familiar types and their constructs, e.g. products and function spaces, as well as their effective counterparts. Aspects of this program in topology and analysis are going to be the focus of the thesis of Andrej Bauer [7]. The remainder of this proposal is organized as follows. First we give a brief historical overview in Section 2 and then in Section 3 we recall the notion of a partial combinatory algebra. In Section 4 we outline the logic of realizability and modality by first, in Subsection 4.1, giving a ....

....g. Then (I ; I ) is a type of RT(P) because I is easily seen to be realized to be symmetric and transitive. For instance, for symmetry, we have to show that there exists a realizer in Pwhich, for all [x 1 ] and [x 2 ] in I , realizes the formula [x 1 ] I [x 2 ] oe [x 2 ] I [x 1 ] 9 See [7] for a host of examples. 10 Categorically speaking there is a full and faithful embedding of the category PER(P) into the topos RT(P N) But surely the identity x:x is such a realizer. For transitivity, we have to show that there exists a realizer in P which realizes the formula [x 1 ] I [x ....

A. Bauer. Topology and computability. Thesis Proposal, April 1998.

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