caa a22 4500 388039116 CHVBK 20180307125016.0 cr unu---uuuuu 161130e199812 xx s 000 0 eng 10.2307/2586655 doi S0022481200014304 pii (NATIONALLICENCE)cambridge-10.2307/2586655 Compactness of Lobe spaces [Elektronische Daten] 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]. Copyright © Association for Symbolic Logic 1998 Jin Renling Department of Mathematics, College of Charleston, Charleston, SC 29424, USA. E-mail: jinr@cofc.edu Shelah Saharon Institute of Mathematics, The Hebrew University, Jerusalem, Israel. E-mail: shelah@math.huji.ac.il The Journal of Symbolic Logic Cambridge University Press 63/4(1998-12), 1371-1392 0022-4812 63:4<1371 1998 63 JSL https://doi.org/10.2307/2586655 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586655 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jin Renling Department of Mathematics, College of Charleston, Charleston, SC 29424, USA. E-mail: jinr@cofc.edu NATIONALLICENCE 700 1- Shelah Saharon Institute of Mathematics, The Hebrew University, Jerusalem, Israel. E-mail: shelah@math.huji.ac.il NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/4(1998-12), 1371-1392 0022-4812 63:4<1371 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge