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Title of Journal: Arch Math Logic

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Abbravation: Archive for Mathematical Logic

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Springer-Verlag

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10.1002/chin.201606219

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1432-0665

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Register computations on ordinals

Authors: Peter Koepke Ryan Siders
Publish Date: 2008/07/19
Volume: 47, Issue: 6, Pages: 529-548
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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 ZermeloFraenkel 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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