A01=Philipp Rothmaler
Abelian Groups
ACF
Algebraic Closure
Atomic Formulas
Author_Philipp Rothmaler
Category=PBCD
Category=PBF
Category=PBWH
Cofinite Subset
compactness theorem
Deductive Closure
Divisible Abelian Group
Division Ring
Elementary Extension
Elementary Substructure
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
field extension theory
Finite Models
Finite Subset
Finiteness Theorem
first-order logic
Free Variables
Galois Correspondence
Homomorphic Image
Infinite Cardinal
Logically Equivalent
mathematical structures
Non-logical Symbols
Panstwowe Wydawnictwo Naukowe
Peano Arithmetic
Quantifier Elimination
Quantifier Free Formulas
Saturated Models
stability classification
Stone Space
strongly minimal theories applications
ultraproduct technique
Product details
- ISBN 9789056993139
- Weight: 580g
- Dimensions: 152 x 229mm
- Publication Date: 31 Oct 2000
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect.
This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct 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, 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 theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
