Lectures on algebraic model theory / Bradd Hart; Matthew Valeriote, eds.

Hart, Bradd T. *1960-* [Hrsg.] ; Valeriote, Matthew

English

Providence, R.I : American Mathematical Society, c 2002

VII, 111 S : Ill., graph. Darst ; 27 cm

12001-53718

Includes bibliographical references

Online-Ausg.: Lectures on algebraic model theory. - Providence, R.I : American Mathematical Society, 2012. - Online-Ressource (1 online resource (vii, 111 p. : ill.))

978-0-8218-2705-5

0-8218-2705-7 (alk. paper)

12001-53718

Machine generated contents note: Lecture Series 1. Differential Fields 1 -- Anand Pillay -- Chapter 1. Differential Fields 3 -- 1.1 Basics 3 -- Dimension theory 8 -- 1.2 Varieties, differential varieties and tangent bundles 18 -- Varieties 18 -- Differential varieties 19 -- Tangent spaces and abstract varieties 20 -- Differential forms 23 -- 1.3 Strongly minimal sets of d-degree 1 27 -- 1.4 Kolchin's logarithmic derivative 31 -- 1.5 Prologations, torsors and the Buium-Manin homomorphism 35 -- Algebraic groups: Geometry 37 -- 1.6 Manin's construction 40 -- Bibliography 45 -- Lecture Series 2. Lectures on o-Minimality 47 -- Patrick Speissegger -- Chapter 1. Lectures on o-Minimality 49 -- 1.1 Adding exponentiation 49 -- 1.2 T-convexity and tame extensions 52 -- 1.3 Piecewise linearity 56 -- 1.4 The Wilkie inequality 58 -- 1.5 The valuation property 61 -- Bibliography 65 -- Lecture Series 3. Tame Congrugence Theory 67 -- Matthias Clasen and Matthew Valeriote -- Chapter 1. The Structure of Finite Algebra 69 -- 1.1 Palfy's theorem 69 -- 1.2 Localization and relativization 72 -- 1.3 Centrality 79 -- 1.4 Labelled congruence lattices 87 -- Chapter 2. Varieties 89 -- 2.1 Subdirectly irreducibles 89 -- 2.2 Facts about the abelian condition 92 -- 2.3 The case typ(0, p) = 2 94 -- 2.4 The case typ{S} = {1} 95 -- 2.5 The residually large configuration 97 -- 2.6 The case type{S} = {1, 2} 102 -- 2.7 Multitraces 104 -- 2.8 Parallelism 107 -- Bibliography 113

*Algebra / Modelltheorie

*Algebraische Modelltheorie

*Modelltheorie / Algebraischer Körper

*Model theory ; Algebraic fields ; Model theory ; Algebraic fields

*Model theory ; Algebraic fields

Library of Congress Classification: QA9.7.H37 2001 ; QA9.7

Dewey Decimal Classification: 511.3

Regensburger Verbund-Klassifikation: SK 130: Logik und Grundlagen, Metamathematik,

Mathematics Subject Classification: *00B25

Mathematics Subject Classification: 03-06

Mathematics Subject Classification: 12-06

Machine generated contents note: Lecture Series 1. Differential Fields 1 -- Anand Pillay -- Chapter 1. Differential Fields 3 -- 1.1 Basics 3 -- Dimension theory 8 -- 1.2 Varieties, differential varieties and tangent bundles 18 -- Varieties 18 -- Differential varieties 19 -- Tangent spaces and abstract varieties 20 -- Differential forms 23 -- 1.3 Strongly minimal sets of d-degree 1 27 -- 1.4 Kolchin's logarithmic derivative 31 -- 1.5 Prologations, torsors and the Buium-Manin homomorphism 35 -- Algebraic groups: Geometry 37 -- 1.6 Manin's construction 40 -- Bibliography 45 -- Lecture Series 2. Lectures on o-Minimality 47 -- Patrick Speissegger -- Chapter 1. Lectures on o-Minimality 49 -- 1.1 Adding exponentiation 49 -- 1.2 T-convexity and tame extensions 52 -- 1.3 Piecewise linearity 56 -- 1.4 The Wilkie inequality 58 -- 1.5 The valuation property 61 -- Bibliography 65 -- Lecture Series 3. Tame Congrugence Theory 67 -- Matthias Clasen and Matthew Valeriote -- Chapter 1. The Structure of Finite Algebra 69 -- 1.1 Palfy's theorem 69 -- 1.2 Localization and relativization 72 -- 1.3 Centrality 79 -- 1.4 Labelled congruence lattices 87 -- Chapter 2. Varieties 89 -- 2.1 Subdirectly irreducibles 89 -- 2.2 Facts about the abelian condition 92 -- 2.3 The case typ(0, p) = 2 94 -- 2.4 The case typ{S} = {1} 95 -- 2.5 The residually large configuration 97 -- 2.6 The case type{S} = {1, 2} 102 -- 2.7 Multitraces 104 -- 2.8 Parallelism 107 -- Bibliography 113

http://www.loc.gov/catdir/toc/fy022/2001053718.html [Table of contents]

https://zbmath.org/?q=an:0980.00023 [Zentralblatt MATH]

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