Chatzidakis Z.M., Macpherson D., Pillay A., Wilkie A. (Eds.) Model theory with applications to algebra and analysis. Volume 1

Cambridge University Press, 2008. — 351 p. — (London Mathematical Society Lecture Note volume 349). — ISBN 13 9780521694841.Теория моделей с приложениями к алгебре и анализу. Том 1The 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.
Model theory and stability theory, with applications in differential algebra and algebraic geometryDifferential 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 K¨ahler geometry
local definability theory for holomorphic functions
Some observations about the real and imaginary parts of complex Pfaffian functions 2
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