A Turing machine model for Kleene Type 2 recursion
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 AFL2020 is an example of Kleene Recursion in 2E. An application of Gandy Selection in the feedback setting solves questions there raised on uniformly finding indices for recursive unions etc. of feedback semi-computable sets; further it allows for effective choice and other principles.
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