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Books > Science & Mathematics > Mathematics > Algebra
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Introduction to Model Theory (Paperback, New Ed)
Loot Price: R2,357
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Introduction to Model Theory (Paperback, New Ed)
Series: Algebra, Logic and Applications
Expected to ship within 9 - 15 working days
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Model theory investigates mathematical structures by means of
formal languages. These so-called first-order languages have proved
particularly useful. The text introduces the reader to the model
theory of first-order logic, avoiding syntactical issues that are
not too relevant to model-theory. In this spirit, the compactness
theorem is proved via the algebraically useful ultraproduct
technique, rather than via the completeness theorem of first-order
logic. This leads fairly quickly to algebraic applications, like
Malcev's local theorems (of group theory) and, after a little more
preparation, also to Hilbert's Nullstellensatz (of field theory).
Steinitz' dimension theory for field extensions is obtained as a
special case of a much more general model-theoretic treatment of
strongly minimal sets. The final chapter is on the models of the
first-order theory of the integers as an abelian group. This
material appears here for the first time in a textbook of
introductory level, and is used to give hints to further reading
and to recent developments in the field, such as stability (or
classification) theory. The latter itself is not touched upon. The
undergraduate or graduate, is assumed t
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