Book contents
- Frontmatter
- Contents
- Preface
- Contributors
- Model theory and stability theory, with applications in differential algebra and algebraic geometry
- Differential algebra and generalizations of Grothendieck's conjecture on the arithmetic of linear differential equations
- Schanuel's conjecture for non-isoconstant elliptic curves over function fields
- An afterthought on the generalized Mordell-Lang conjecture
- On the definitions of difference Galois groups
- Differentially valued fields are not differentially closed
- Complex analytic geometry in a nonstandard setting
- Model theory and Kähler geometry
- Some local definability theory for holomorphic functions
- Some observations about the real and imaginary parts of complex Pfaffian functions
- Fusion of structures of finite Morley rank
- Establishing the o-minimality for expansions of the real field
- On the tomography theorem by P. Schapira
- A class of quantum Zariski geometries
- Model theory guidance in number theory?
Preface
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- Preface
- Contributors
- Model theory and stability theory, with applications in differential algebra and algebraic geometry
- Differential algebra and generalizations of Grothendieck's conjecture on the arithmetic of linear differential equations
- Schanuel's conjecture for non-isoconstant elliptic curves over function fields
- An afterthought on the generalized Mordell-Lang conjecture
- On the definitions of difference Galois groups
- Differentially valued fields are not differentially closed
- Complex analytic geometry in a nonstandard setting
- Model theory and Kähler geometry
- Some local definability theory for holomorphic functions
- Some observations about the real and imaginary parts of complex Pfaffian functions
- Fusion of structures of finite Morley rank
- Establishing the o-minimality for expansions of the real field
- On the tomography theorem by P. Schapira
- A class of quantum Zariski geometries
- Model theory guidance in number theory?
Summary
These two volumes contain both expository and research papers in the general area of model theory and its applications to algebra and analysis. The volumes grew out of the semester on “Model Theory and Applications to Algebra and Analysis” which took place at the Isaac Newton Institute (INI), Cambridge, from January to July 2005. We, the editors, were also the organizers of the programme. The contributors have been selected from among the participants and their papers reflect many of the achievements and advances obtained during the programme. Also some of the expository papers are based on tutorials given at the March-April 2005 training workshop. We take this opportunity, both as editors of these volumes and organizers of the MAA programme, to thank the Isaac Newton Institute and its staff for supporting our programme and providing a perfect environment for mathematical research and collaboration.
The INI semester saw activity and progress in essentially all areas on the “applied” side of model theory: o-minimality, motivic integration, groups of finite Morley rank, and connections with number theory and geometry. With the exception of motivic integration and valued fields, these topics are well represented in the two volumes.
The collection of papers is more or less divided into (overlapping) themes, together with a few singularities. Aspects of the interaction between stability theory, differential and difference equations, and number theory, appear in the first six papers of volume I.
- Type
- Chapter
- Information
- Model Theory with Applications to Algebra and Analysis , pp. ix - xiiPublisher: Cambridge University PressPrint publication year: 2008