Finn Lawler thesis outline (Rev #2, changes)

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This page is for material relevant to my Ph.D. thesis — I will try to sketch the important bits here as I write up the document itself.

Pages:

Chapter 2

There are two quite different ways to construct the effective topos: we start with the Kleene algebra (,)(\mathbb{N}, \cdot) of partial recursive functions, and then

  1. construct the effective tripos,

    • this is the hyperdoctrine over SetSet whose predicates over XX are \mathbb{N}-valued sets XPX \to P\mathbb{N}, ordered by ϕψ\phi \leq \psi if there exists a partial recursive function Φ\Phi such that for any xXx \in X and nϕxn \in \phi x, Φn\Phi n is defined and contained in ψx\psi x.

    and then take its category of partial equivalence relations; or

  2. construct the regular category of assemblies over \mathbb{N}

    and take its exact completion.

We show how the two are related.

Revision on November 22, 2012 at 23:02:11 by Finn Lawler?. See the history of this page for a list of all contributions to it.