内集理论中的非标准船体构造与Loeb测度

K. Hrbacek, M. Katz
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引用次数: 4

摘要

摘要目前比较流行的两种实践鲁滨逊非标准分析的方法是模型理论方法和公理/句法方法。有时声称内部公理化方法不能处理依赖于外部集合的构造。我们表明,内部框架提供了非标准船体和勒布措施的成功帐户。这项工作所依赖的基本事实是,标准超滤器对标准宇宙的超功率与内部宇宙的子宇宙自然同构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
CONSTRUCTING NONSTANDARD HULLS AND LOEB MEASURES IN INTERNAL SET THEORIES
Abstract Currently the two popular ways to practice Robinson’s nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions relying on external sets. We show that internal frameworks provide successful accounts of nonstandard hulls and Loeb measures. The basic fact this work relies on is that the ultrapower of the standard universe by a standard ultrafilter is naturally isomorphic to a subuniverse of the internal universe.
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