Model theory with applications to algebra and analysis / Zoé Chatzidakis [and others]
Account of current research in model theory and its connections with algebra and analysis; contributions from leaders in the field.
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| Online Access: |
Full Text (via ProQuest) |
|---|---|
| Other Authors: | |
| Other title: | Model theory and applications to algebra and analysis. |
| Format: | eBook |
| Language: | English |
| Published: |
Cambridge, UK ; New York :
Cambridge University Press,
2008.
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| Series: | London Mathematical Society lecture note series ;
349-350. |
| Subjects: |
Table of Contents:
- Cover; Title; Copyright; Contents; Preface; Contributors; Model theory and stability theory, with applications in differential algebra and algebraic geometry; 1 Model theory; The reals.; Algebraically closed fields; Differentially closed fields.; Many-sorted structures; 2 Stability; Independence (also called nondividing, nonforking).; Stationarity; Morley rank and t.t. theories.; Algebraic examples.; Differentially closed fields continued.; Theories/structures of finite Morley rank.; 3 Modularity; 4 Algebraic varieties over differential fields; Linear differential equations.
- 5 The strong conjecture for DReferences; Differential algebra and generalizations of Grothendieck's conjecture on the arithmetic of linear differential equations; Summary; 1 Introduction; 2 Differential algebra; 3 Integrability, connections, principal bundles; 4 Proof of main result; References; Schanuel's conjecture for non-isoconstant elliptic curves over function fields; Summary; Introduction; 1 Constant semi-abelian varieties; 2 Arithmetic interlude; 3 Non-isoconstant semi-abelian surfaces; References; An afterthought on the generalized Mordell-Lang conjecture; Summary; 1 Introduction.
- Basic notational conventions2 Preliminaries; 3 Proof of ( * *); References; On the definitions of difference Galois groups; Summary; 1 Introduction; 2 A Ring-Theoretic Point of View; 3 A Tannakian Point of View; 3.1 The action of Aut(CK/C) on {{MK}}; 3.2 Another fiber functor ̃!M for {{MK}}; 3.3 Comparison of the Galois groups; 4 A Model-Theoretic Point of View; 4.1 Preliminary model-theoretic definitions and results; 4.2 The Galois group; 4.3 More on Picard-Vessiot rings; 4.4 Concluding remarks; References; Differentially valued fields are not differentially closed; Summary; 1 Introduction.
- 2 Logarithmic derivatives and differential valuationsReferences; Complex analytic geometry in a nonstandard setting; Summary; 1 Introduction; 2 Topological preliminaries; 2.1 "Real" and "complex" dimensions; 2.2 Locally closed sets and definably proper maps; 2.3 Linear and affine subspaces; 2.4 Generic projections; 2.5 The main covering theorem; 3 K-manifolds and submanifolds; 4 K-analytic sets; 5 K-analytic subsets of Kn; Chow's Theorem; 6 The set of singular points; 7 Dimension, rank and Remmert's Theorem; 8 K-manifolds as Zariski structures; 8.1 Locally modular elliptic curves.
- 9 Meromorphic maps10 Campana-Fujiki; 11 A finite version of the coherence theorem; 12 Appendix; References; Model theory and K ̈ahler geometry; Summary; 1 Introduction; 2 Preliminaries on complex forms; 3 Saturation and K ̈ahler manifolds; 4 Holomorphic forms on K ̈ahler manifolds; 5 Stability theory and K ̈ahler manifolds; 6 Local Torelli and the isotriviality theorem; References; Some local definability theory for holomorphic functions; Summary; 1 Introduction; 1.1 Problem.; 1.2 Differentiation.; 1.3 Schwarz Reflection.; Definition 1.4; 1.5 Implicit Definability; 1.6 Composition; Definition 1.7.