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Basic Model Theory
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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
  • ISBN-10: 1575860481
  • ISBN-13: 978-1575860480
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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 first-order languages, the model theory of which is best known.

An example result is Lowenheim's theorem (the oldest in the field): a first-order sentence true of some uncountable structure must hold in some countable structure as well. Second-order 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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