Journal of Symbolic Logic

Compactness of Loeb Spaces

Renling Jin and Saharon Shelah

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In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In $\S1$ we prove that Loeb spaces are compact under various assumptions, and in $\S2$ we prove that Loeb spaces are not compact under various other assumptions. The results in $\S1$ and $\S2$ give a quite complete answer to a question of D. Ross in [9], [11] and [12].

Article information

J. Symbolic Logic, Volume 63, Issue 4 (1998), 1371-1392.

First available in Project Euclid: 6 July 2007

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Zentralblatt MATH identifier


Primary: 28E05: Nonstandard measure theory [See also 03H05, 26E35]
Secondary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 03E35: Consistency and independence results


Jin, Renling; Shelah, Saharon. Compactness of Loeb Spaces. J. Symbolic Logic 63 (1998), no. 4, 1371--1392.

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