Symmetry for transfinite computability

TL;DR

This paper explores restoring symmetry in transfinite computation models, similar to finite Turing machines, by examining models within constructible universes, revealing independence from classical set theories.

Contribution

It introduces a new model of transfinite computation that recovers the symmetry between inputs, outputs, programs, time, and storage, akin to finite Turing computation.

Findings

Model exhibits symmetry in constructible universes

Symmetry independence from classical set theory

Insights into transfinite computational structures

Abstract

Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model of computation. This model exhibits the same symmetry as finite Turing computation in universes constructible from a set of ordinals, but that statement is independent of von Neumann-G\"odel-Bernays class theory.