Register computations on ordinals

Archive for Mathematical Logic 47 (6):529-548 (2008)

Abstract

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 Gödel’s constructible universe L

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References found in this work

The Consistency of the Continuum Hypothesis.Kurt Godel - 1940 - Princeton University Press.
Infinite Time Turing Machines.Joel Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
Turing Computations on Ordinals.Peter Koepke - 2005 - Bulletin of Symbolic Logic 11 (3):377-397.

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