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Compactness of Lobe spaces

Published online by Cambridge University Press:  12 March 2014

Renling Jin
Affiliation:
Department of Mathematics, College of Charleston, Charleston, SC 29424, USA. E-mail:jinr@cofc.edu Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. E-mail:jinr@cofc.edu
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel. E-mail:shelah@math.huji.ac.il Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. E-mail:shelah@math.huji.ac.il Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA. E-mail:shelah@math.huji.ac.il

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].

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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