Symmetry for transfinite computability

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.