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

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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DOI 10.2307/2275513
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References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Non-Standard Analysis.Gert Heinz Müller - 1969 - Journal of Symbolic Logic 34 (2):292-294.
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.
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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Citations of this work BETA

Quantum Set Theory: Transfer Principle and De Morgan's Laws.Masanao Ozawa - 2021 - Annals of Pure and Applied Logic 172 (4):102938.
The Trend of Logic and Foundation of Mathematics in Japan in 1991 to 1996.Yuzuru Kakuda, Kanji Namba & Nobuyoshi Motohashi - 1997 - Annals of the Japan Association for Philosophy of Science 9 (2):95-110.

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