Compactness of a Loeb space

Renling Jin*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 §1 we prove that Loeb spaces are compact under various assumptions, and in §2 we prove that Loeb spaces are not compact under various other assumptions. The results in §1 and §2 give a quite complete answer to a question of D. Ross in [9], [11] and [12].

Original languageEnglish
Pages (from-to)1371-1392
Number of pages22
JournalJournal of Symbolic Logic
Volume63
Issue number4
DOIs
StatePublished - Dec 1998

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