Model theory with applications to algebra and analysis,

✍ Scribed by Chatzidakis Z.M., et al. (eds.)

• Publisher: CUP
• Year: 2008
• Tongue: English
• Leaves: 351
• Series: London Mathematical Society Lecture Note Series
• Category: Library

✦ Synopsis

The first of a two-volume set showcasing the current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. This volume begins with a series of expository essays and research papers around the subject matter of a Newton Institute Semester on Model Theory and Applications to Algebra and Analysis. The articles included showcase outstanding new research on topics such as model theory and conjectures around Mordell-Lang; arithmetic of differential equations, and Galois Theory of difference equations; model theory and complex analytic geometry; o-minimality; model theory and noncommutative geometry; definable groups of finite dimension; Hilbert's tenth problem; and Hrushovski constructions. With contributions from so many leaders in the field, this two-volume set will undoubtedly appeal to all mathematicians with an interest in model theory and its applications.

✦ Table of Contents

Table of contents for Volume 1......Page 6
Table of contents for Volume 2......Page 8
Preface......Page 10
Contributors......Page 14
Model theory and stability theory, with applications in di erential algebra and algebraic geometry......Page 18
Differential algebra and generalizations of Grothendieck’s conjecture
on the arithmetic of linear differential equations......Page 42
Schanuel’s conjecture for non-isoconstant elliptic curves over function elds......Page 58
An afterthought on the generalized Mordell-Lang conjecture......Page 80
On the definitions of difference Galois groups......Page 90
Differentially valued fields are not differentially closed......Page 128
Complex analytic geometry in a nonstandard setting......Page 134
Model theory and Kähler geometry......Page 184
Some local definability theory for holomorphic functions......Page 214
Some observations about the real and imaginary parts of complex Pfaffian functions......Page 232
Fusion of structures of finite Morley rank......Page 242
Establishing the o-minimality for expansions of the real field......Page 266
On the tomography theorem by P. Schapira......Page 300
A class of quantum Zariski geometries......Page 310
Model theory guidance in number theory?......Page 344