Register computations on ordinals

We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are 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. This allows the following characterization of computable sets: a set of ordinals is ordinal register computable if and only if it is an element of G

• Type: Journal
• Year: 2008
• Where: AML
• Authors: Peter Koepke, Ryan Siders
• Keywords: AML 2008, Ordinal Register, Ordinal Register Machines, Register Machine