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CONTINUOUS SENTENCES PRESERVED UNDER REDUCED PRODUCTS

Part of: Model theory

Published online by Cambridge University Press:  07 September 2020

ISAAC GOLDBRING  and
H. JEROME KEISLER
ISAAC GOLDBRING
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, IRVINE 340 ROWLAND HALL (BLDG.# 400), IRVINE, CA92697-3875, USAE-mail: isaac@math.uci.edu
H. JEROME KEISLER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN 480 LINCOLN DRIVE, MADISONWI53706, USAE-mail: keisler@math.wisc.edu
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Abstract

Answering a question of Cifú Lopes, we give a syntactic characterization of those continuous sentences that are preserved under reduced products of metric structures. In fact, we settle this question in the wider context of general structures as introduced by the second author.

Keywords

reduced productscontinuous logic

MSC classification

Primary: 03C20: Ultraproducts and related constructions
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 2 , June 2022 , pp. 649 - 681
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Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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