Basic Model Theory (Studies in Logic, Language, and Information) 1st Edition by Kees Doets (PDF)

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 Löwenheim’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.

User’s Reviews

Editorial Reviews: 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. 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book takes you by the hand through the development of formal model theory. All the chapters present the basic treatment of the theory except for the 3rd, which was on Ehrenfught-Fraisse Games and how they fit into comparing models. I could do without that chapter. For the most part, the writing is short, concise, and a good account of all the more popular theorems of the theory. It’s a handy reference for reading other, more laborious reads written in the subject.

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