Kossak, Roman City University of New York
Schmerl, James University of Connecticut, Storrs
Print publication date: 2006 (this edition)
Published to Oxford Scholarship Online: September 2007
Print ISBN-13: 978-0-19-856827-8







doi:10.1093/acprof:oso/9780198568278.003.0001

Roman Kossak
James H. Schmerl
Abstract: This introductory chapter covers a wide range of topics, from basic notational conventions and coding in arithmetic to important classical results. The well-known theorems, such as Gaifman's splitting theorem, Arithmetized Completeness Theorem, or Friedman's Embedding Theorem are discussed without proofs. Proofs are given for less known facts, like Blass-Gaifman and Ehrenfeucht lemmas. The chapter also presents a systematic introduction to recursively and arithmetically saturated models, resplendent models, and satisfaction classes.

Keywords: coding in arithmetic, Blass-Gaifman Lemma, Ehrenfeucht Lemma, arithmetic saturation,

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