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arXiv · 2606.24664

A Turing machine model for Kleene Type 2 recursion

Philip D Welch
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Abstract

We give an account of Kleene's Type 2 recursion theory modelled on Turing machines. We apply this account to observe that the feedback computation of \cite{AFL2020} is an example of Kleene Recursion in $^2\mathsf{E}$. An application of Gandy Selection in the feedback setting solves questions there raised on uniformly finding indices for recursive unions {\em etc.} of feedback semi-computable sets; further it allows for effective choice and other principles.

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Philip D Welch. 2026-06-23. A Turing machine model for Kleene Type 2 recursion. https://arxiv.org/abs/2606.24664

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