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12

CIE
2005
Springer

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Computing a Model of Set Theory

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Computing a Model of Set Theory

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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.

Peter Koepke

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Arbitrary Ordinal Length | CIE 2005 | Ordinal Computability | Truth Predicate |

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Added	26 Jun 2010
Updated	26 Jun 2010
Type	Conference
Year	2005
Where	CIE
Authors	Peter Koepke

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