Relative computability in the effective topos
Published online by Cambridge University Press: 24 October 2008
Extract
Let ℕ be the natural numbers object in , the effective topos. It was shown in [1] that the maps ℕ → ℕ are (internally or externally) just the total recursive functions. Now a subset A ⊆ ω of natural numbers corresponds to a ¬¬-closed subobject A ↣ ℕ; let kA be the least topology forcing A to be decidable, and let ℕA be the sheafification of ℕ with respect to this topology. Then one would expect the maps ℕ → ℕA to be the total functions recursive in A.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 3 , November 1989 , pp. 419 - 422
- Copyright
- Copyright © Cambridge Philosophical Society 1989
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