Annals of Pure and Applied Logic 98 (1-3):157-171 (1999)

Abstract
Three results in [14] and one in [8] are analyzed in Sections 3–6 in order to supply examples on Loeb probability spaces, which distinguish the different strength among three generalizations of k-saturation, as well to answer some questions in Section 7 of [15]. In Section 3 we show that not every automorphism of a Loeb algebra is induced by an internal permutation, in Section 4 we show that if the 1-special model axiom is true, then every automorphism of a Loeb algebra is induced by a point-automorphism, in Section 5 we show that not every measure-preserving homomorphism from a small subalgebra to a Loeb algebra is induced by an internal permutation, without assuming full-saturation, in Section 6 we show that, under some cardinality assumptions, the 1-isomorphism property does not guarantee the compactness of a Loeb space, and in Section 7 an application of the 1-special model axiom is given on the existence of ergodic transformations of a Loeb space, which partially answers Problem 2.3 of [5]
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DOI 10.1016/s0168-0072(98)00055-4
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References found in this work BETA

The Isomorphism Property Versus the Special Model Axiom.Renling Jin - 1992 - Journal of Symbolic Logic 57 (3):975-987.
The Special Model Axiom in Nonstandard Analysis.David Ross - 1990 - Journal of Symbolic Logic 55 (3):1233-1242.
A Theorem on the Isomorphism Property.Renling Jin - 1992 - Journal of Symbolic Logic 57 (3):1011-1017.
The Strength of the Isomorphism Property.Renling Jin & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):292-301.

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Citations of this work BETA

Maharam Spectra of Loeb Spaces.Renling Jin & H. Jerome Keisler - 2000 - Journal of Symbolic Logic 65 (2):550-566.
Combinatorial Principles in Nonstandard Analysis.Mauro Di Nasso & Karel Hrbacek - 2003 - Annals of Pure and Applied Logic 119 (1-3):265-293.

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