A Universal Hypercomputer

Andrew Powell

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arXiv · 1806.08747

A Universal Hypercomputer

Andrew Powell

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Abstract

This paper describes a type of infinitary computer (a hypercomputer) capable of computing truth in initial levels of the set theoretic universe, V. The proper class of such hypercomputers is called a universal hypercomputer. There are two basic variants of hypercomputer: a serial hypercomputer and a parallel hypercomputer. The set of computable functions of the two variants is identical but the parallel hypercomputer is in general faster than a serial hypercomputer (as measured by an ordinal complexity measure). Insights into set theory using information theory and a universal hypercomputer are possible, and it is argued that the Generalised Continuum Hypothesis can be regarded as a information-theoretic principle, which follows from an information minimisation principle.

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Andrew Powell. 2018-06-22. A Universal Hypercomputer. https://arxiv.org/abs/1806.08747

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