Computing a Model of Set Theory

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. The generalized Turing machine is able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals in a model of the Zermelo-Fraenkel axioms ZFC. Hence a set of ordinals is ordinal computable from ordinal parameters if and only if it is an element of G¨odel’s constructible universe L.

• Type: Conference
• Year: 2005
• Where: CIE
• Authors: Peter Koepke
• Keywords: Arbitrary Ordinal Length, CIE 2005, Ordinal Computability, Truth Predicate