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Reduced products and sheaves of metric structures
Author(s) -
Lopes Vinicius Cifú
Publication year - 2013
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201200084
Subject(s) - sheaf , mathematics , metric (unit) , metric space , pure mathematics , product (mathematics) , space (punctuation) , algebra over a field , discrete mathematics , computer science , geometry , business , marketing , operating system
We introduce reduced products in continuous logic, and provide ways to establish satisfaction in the reduced product based on the satisfaction in its fibers, and conversely, on the lines that Horn and Chang did for reduced products in classical logic. We also consider a definition of a sheaf of metric structures, endow its stalks with a metric prestructure, and determine what filters can be used so that a collection of reduced products of arbitrary structures forms a sheaf on a given index space.