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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 <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600058-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600058:malq201600058-math-0001\" \/> and Abstract Elementary Classes, respectively). We also translate various notions of classification theory.<\/jats:p>","DOI":"10.1002\/malq.201600058","type":"journal-article","created":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T13:02:44Z","timestamp":1512046964000},"page":"397-414","source":"Crossref","is-referenced-by-count":3,"title":["A presentation theorem for continuous logic and metric abstract elementary classes"],"prefix":"10.1002","volume":"63","author":[{"given":"Will","family":"Boney","sequence":"first","affiliation":[{"name":"Department of Mathematics Harvard University 1 Oxford Street Cambridge MA 02138 United States of America"}]}],"member":"311","published-online":{"date-parts":[[2017,11,30]]},"reference":[{"key":"e_1_2_9_2_1","unstructured":"N.Ackerman Encoding complete metric structures by classical structures submitted."},{"key":"e_1_2_9_3_1","volume-title":"Categoricity, University Lecture Series","author":"Baldwin J.","year":"2009"},{"key":"e_1_2_9_4_1","volume-title":"Model theory for metric structures, in: Model Theory with Applications to Algebra and Analysis","author":"Ben\u2010Yaacov I.","year":"2008"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1122038916"},{"key":"e_1_2_9_6_1","volume-title":"Advances in Classification Theory for Abstract Elementary Classes","author":"Boney W.","year":"2014"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2014.30"},{"key":"e_1_2_9_8_1","unstructured":"W.Boney The \u0393\u2010ultraproduct and averageable classes preprint 2015(arXiv:1511.00982)."},{"key":"e_1_2_9_9_1","unstructured":"W.BoneyandP.Zambrano Around the set\u2010theoretical consistency ofd\u2010tameness of Metric Abstract Elementary Classes preprint 2015(arXiv:1508.05529)."},{"key":"e_1_2_9_10_1","volume-title":"Some remarks on the model theory of infinitary languages, in: The Syntax and Semantics of Infinitary Languages","author":"Chang C. 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