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Finitistic Properties of High Complexity (1707.05772v1)
Published 18 Jul 2017 in math.LO
Abstract: We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order arithmetical truth and beyond. Since the predicates are interpreted using properties of certain natural finite structures, they are arguably finitistic.
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