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A presentation theorem for continuous logic and metric abstract elementary classes
Author(s) -
Boney Will
Publication year - 2017
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.201600058
Subject(s) - mathematics , metric space , metric (unit) , scope (computer science) , set (abstract data type) , presentation (obstetrics) , space (punctuation) , algebra over a field , discrete mathematics , pure mathematics , computer science , medicine , operations management , economics , radiology , programming language , operating system
In recent years, model theory has widened its scope to include metric structures by considering real‐valued models whose underlying set is a complete metric space. We show that it is possible to carry out this work by giving presentation theorems that translate the two main frameworks (continuous first order logic and Metric Abstract Elementary Classes) into discrete settings (a nice fragment of L ω 1 , ωand Abstract Elementary Classes, respectively). We also translate various notions of classification theory.