Scott incomplete Boolean ultrapowers of the real line

Journal of Symbolic Logic 60 (1):160-171 (1995)
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Abstract

An ordered field is said to be Scott complete iff it is complete with respect to its uniform structure. Zakon has asked whether nonstandard real lines are Scott complete. We prove in ZFC that for any complete Boolean algebra B which is not (ω, 2)-distributive there is an ultrafilter U of B such that the Boolean ultrapower of the real line modulo U is not Scott complete. We also show how forcing in set theory gives rise to examples of Boolean ultrapowers of the real line which are not Scott complete

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10.2307/2275513

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References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
The theory of Boolean ultrapowers.Richard Mansfield - 1971 - Annals of Mathematical Logic 2 (3):297-323.
Forcing in nonstandard analysis.Masanao Ozawa - 1994 - Annals of Pure and Applied Logic 68 (3):263-297.
Remarks on the nonstandard real axis.Elias Zakon - 1969 - In W. A. J. Luxemburg (ed.), Applications of model theory to algebra, analysis, and probability. New York,: Holt, Rinehart and Winston. pp. 195--227.

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