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Scott incomplete Boolean ultrapowers of the real line

Published online by Cambridge University Press:  12 March 2014

Masanao Ozawa
Masanao Ozawa*
Affiliation:
Department of Mathematics, College of General Education, Nagoya University, Nagoya 464-01, Japan, E-mail: e43252a@nucc.cc.nagoya-u.ac.jp
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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 of B such that the Boolean ultrapower of the real line modulo 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 1 , March 1995 , pp. 160 - 171
Copyright
Copyright © Association for Symbolic Logic 1995

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References

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