Ordinals, Computations, and Models of Set Theory
نویسنده
چکیده
Ordinary computations can be characterised by register machines working with natural numbers. We study ordinal register machines where the registers can hold arbitrary ordinal numbers. The class of sets of ordinals which are computable by such machines has strong closure properties and satisfies the set theoretic axiom system SO. This implies that ordinal computability is equivalent to Gödel’s model L of constructible sets. In this tutorial we shall give a proof of this theorem, starting with brief reviews of ordinal theory and standard register machines.
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