Scott incomplete Boolean ultrapowers of the real line

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

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