Titlebook: A Guide to Classical and Modern Model Theory; Annalisa Marcja,Carlo Toffalori Book 2003 Springer Science+Business Media New York 2003 alge

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Annalisa Marcja,Carlo ToffaloriIncludes supplementary material:

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A Guide to Classical and Modern Model Theory978-94-007-0812-9Series ISSN 1572-6126 Series E-ISSN 2212-7313

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Cesare Parenti,Alberto Parmeggianition also in Chapter 2, where we considered its connection with quantifier elimination and completeness. But now we wish to examine model completeness in a closer and more direct way, to discuss its genesis and motivations, as well as its importance and applications.

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The Syntax and Semantics of ,CRL,m is very simple to state: for, it says that a theory . categorical in some uncountable power is, consequently, categorical in every uncountable power. This is noteworthy, but perhaps not so dramatic and relevant. However the germs of Morley’s ideas went much further, and their richness permeated the development of Model Theory for several years.

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Cesare Parenti,Alberto Parmeggianifor instance among the models of a given .-theory . For example, in the ordered field of reals (and even in every real closed field), the formula ?(.):.≥0 (being nonnegative) is the same thing as ?′(.):?.(.=.) (being a square). Similarly, in the ordered domain of integers, ?(.):.≥0 (being positive)

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