Compactness of Loeb Spaces
Jin, Renling ; Shelah, Saharon
J. Symbolic Logic, Tome 63 (1998) no. 1, p. 1371-1392 / Harvested from Project Euclid
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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].
Publié le : 1998-12-14
Classification:  28E05,  03H05,  03E35 
@article{1183745636,
     author = {Jin, Renling and Shelah, Saharon},
     title = {Compactness of Loeb Spaces},
     journal = {J. Symbolic Logic},
     volume = {63},
     number = {1},
     year = {1998},
     pages = { 1371-1392},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745636}
}

Jin, Renling; Shelah, Saharon. Compactness of Loeb Spaces. J. Symbolic Logic, Tome 63 (1998) no. 1, pp.  1371-1392. http://gdmltest.u-ga.fr/item/1183745636/