## Journal of Symbolic Logic

### Compactness of Loeb Spaces

#### Abstract

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

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745636

Mathematical Reviews number (MathSciNet)
MR1665731

Zentralblatt MATH identifier
0928.28008

JSTOR