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Compactness of Lobe spaces

Published online by Cambridge University Press:  12 March 2014

Renling Jin  and
Saharon Shelah
Renling Jin
Affiliation:
Department of Mathematics, College of Charleston, Charleston, SC 29424, USA. E-mail:[email protected] Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. E-mail:[email protected]
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel. E-mail:[email protected] Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. E-mail:[email protected] Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA. E-mail:[email protected]
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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
Information
The Journal of Symbolic Logic , Volume 63 , Issue 4 , December 1998 , pp. 1371 - 1392
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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