Exploring the abyss in Kleene’s computability theory
Sam Sanders
Abstract:Kleene’s computability theory based on the S1–S9 computation schemes constitutes a model for computing with objects of any finite type and extends Turing’s ‘machine model’ which formalises computing with real numbers. A fundamental distinction in Kleene’s framework is between normal and non-normal functionals where the former compute the associated Kleene quantifier ∃ n and the latter do not. Historically, the focus was on normal functionals, but recently new non-normal functionals have been studied based on w… Show more
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