Finitistic Properties of High Complexity
Dmytro Taranovsky
TL;DR
This paper explores finitistic models of hypercomputation using sequences and structures, extending the interpretation of non-arithmetic predicates to full second-order arithmetical truth.
Contribution
It introduces finitistic models of hypercomputation based on finite and infinite sequences, extending the scope of interpretability of complex predicates.
Findings
Models reach full second-order arithmetical truth
Predicates are interpreted via properties of natural finite structures
Extends the understanding of finitistic hypercomputation
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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Taxonomy
TopicsComputability, Logic, AI Algorithms · Benford’s Law and Fraud Detection