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 Title Basic Model Theory
 Authors Kees Doets
 Publisher: The Center for the Study of Language and Information Publications (13 Jun. 1996)
 Permission: For personal use
 Paperback: 141 pages
 eBook: PDF (141 pages)
 Language: English
 ISBN10: 1575860481
 ISBN13: 9781575860480
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Book Description
Model theory investigates the relationships between mathematical structures ('models') on the one hand and formal languages (in which statements about these structures can be formulated) on the other. Example structures are: the natural numbers with the usual arithmetical operations, the structures familiar from algebra, ordered sets, etc. The emphasis is on firstorder languages, the model theory of which is best known.
An example result is Lowenheim's theorem (the oldest in the field): a firstorder sentence true of some uncountable structure must hold in some countable structure as well. Secondorder languages and several of their fragments are dealt with as well.
As the title indicates, this book introduces the reader to what is basic in model theory. A special feature is its use of the Ehrenfeucht game by which the reader is familiarised with the world of models.
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