A Universal Hypercomputer

TL;DR

This paper introduces a universal hypercomputer capable of computing truths in set theory's initial universe levels, exploring its variants, computational speed, and implications for set theory and the continuum hypothesis.

Contribution

It defines a universal hypercomputer, compares serial and parallel variants, and links set-theoretic principles to information theory.

Findings

Parallel hypercomputers are generally faster than serial ones.

Universal hypercomputers can compute truths in initial set-theoretic universe levels.

The generalized continuum hypothesis is viewed as an information-theoretic principle.

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.