Computing a Model of Set Theory

机译：计算集合论模型

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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 GOEDEL'S constructible universe L.

机译：通过将长度ω的磁带上的标准TURING可计算性推广到任意序数长度的磁带上的计算，我们定义了序数可计算性的概念。通用的TURING机器能够计算序数上的递归有界真值谓词。可以从真谓词中读出的一组序数满足自然理论SO。 SO是ZERMELO-FRAENKEL公理ZFC模型中一组序数的理论。因此，当且仅当一组序数是GOEDEL可构造宇宙L的元素时，才能根据序数参数进行序数计算。

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来源
《Conference on Computability in Europe(CiE 2005); 20050608-12; Amsterdam(NL)》|2005年|P.223-232|共10页
会议地点 Amsterdam(NL)
作者
Peter Koepke;
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Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universitaet Bonn, Beringstrasse 1, 53113 Bonn, Germany;

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原文格式 PDF
正文语种 eng
中图分类计算技术、计算机技术;
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Computing a Model of Set Theory

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