Guide to Classical and Modern Model Theory

Häftad, Engelska, 2003

1 829 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world.This volume: -is easily accessible to young people and mathematicians unfamiliar with logic; -gives a terse historical picture of Model Theory; -introduces the latest developments in the area; -provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters.A Guide to Classical and Modern Model Theory is for trainees and professional model theorists, mathematicians working in Algebra and Geometry and young people with a basic knowledge of logic.

Produktinformation

Utgivningsdatum2003-06-30
Mått160 x 240 x 21 mm
Vikt576 g
FormatHäftad
SpråkEngelska
SerieTrends in Logic
Antal sidor371
Upplaga2003
FörlagKluwer Academic Publishers
ISBN9781402013317

Tillhör följande kategorier

Matematikens grunder inom Naturvetenskap och teknik

Structures.- 1.1 Structures.- 1.2 Sentences.- 1.3 Embeddings.- 1.4 The Compactness Theorem.- 1.5 Elementary classes and theories.- 1.6 Complete theories.- 1.7 Definable sets.- 1.8 References.- Quantifier Elimination.- 2.1 Elimination sets.- 2.2 Discrete linear orders.- 2.3 Dense linear orders.- 2.4 Algebraically closed fields (and Tarski).- 2.5 Tarski again: Real closed fields.- 2.6 pp-elimination of quantifiers and modules.- 2.7 Strongly minimal theories.- 2.8 o-minimal theories.- 2.9 Computational aspects of q. e.- 2.10 References.- Model Completeness.- 3.1 An introduction.- 3.2 Abraham Robinson’s test.- 3.3 Model completeness and Algebra.- 3.4 p-adic fields and Artin’s Conjecture.- 3.5 Existentially closed structures.- 3.6 DCF0.- 3.7 SCFp and DCFp.- 3.8 ACFA.- 3.9 References.- Elimination of imaginaries.- 4.1 Interpretability.- 4.2 Imaginary elements.- 4.3 Algebraically closed fields.- 4.4 Real closed fields.- 4.5 The elimination of imaginaries sometimes fails.- 4.6 References.- Morley rank.- 5.1 A tale of two chapters.- 5.2 Definable sets.- 5.3 Types.- 5.4 Saturated models.- 5.5 A parenthesis: pure injective modules.- 5.6 Omitting types.- 5.7 The Morley rank, at last.- 5.8 Strongly minimal sets.- 5.9 Algebraic closure and definable closure.- 5.10 References.- ? -stability.- 6.1 Totally transcendental theories.- 6.2 ?-stable groups.- 6.3 ?-stable fields.- 6.4 Prime models.- 6.5 DCF0 revisited.- 6.6 Ryll-Nardzewski’s Theorem, and other things.- 6.7 References.- Classifying.- 7.1 Shelah’s Classification Theory.- 7.2 Simple theories.- 7.3 Stable theories.- 7.4 Superstable theories.- 7.5 ?-stable theories.- 7.6 Classifiable theories.- 7.7 Shelah’s Uniqueness Theorem.- 7.8 Morley’s Theorem.- 7.9 Biinterpretability and Zilber Conjecture.- 7.10 Two algebraicexamples.- 7.11 References.- Model Theory and Algebraic Geometry.- 8.1 Introduction.- 8.2 Algebraic varieties, ideals, types.- 8.3 Dimension and Morley rank.- 8.4 Morphisms and definable functions.- 8.5 Manifolds.- 8.6 Algebraic groups.- 8.7 The Mordell-Lang Conjecture.- 8.8 References.- O-minimality.- 9.1 Introduction.- 9.2 The Monotonicity Theorem.- 9.3 Cells.- 9.4 Cell decomposition and other theorems.- 9.5 Their proofs.- 9.6 Definable groups in o-minimal structures.- 9.7 O-minimality and Real Analysis.- 9.8 Variants on the o-minimal theme.- 9.9 No rose without thorns.- 9.10 References.