Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 63, Issue 4 (1998), 1371-1392.
Compactness of Loeb Spaces
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 ,  and .
J. Symbolic Logic, Volume 63, Issue 4 (1998), 1371-1392.
First available in Project Euclid: 6 July 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.jsl/1183745636