|
Model Theory with Applications to Algebra and Analysis |
|||||||||||||||||||||||||||
|
Edited by Zoé Chatzidakis |
||||||||||||||||||||||||||||
|
The first of a two volume set showcasing
current research in model theory and its
connections with number theory, algebraic
geometry, real analytic geometry and
differential algebra. Each volume contains 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 convey 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 book will
undoubtedly appeal to all mathematicians
with an interest in model theory and its
applications, from graduate students to
senior researchers and from beginners to
experts. Contents |
||||||||||||||||||||||||||||
|
Preface; List of contributors; 1. Model theory and stability theory, with applications in differential algebra and algebraic geometry Anand Pillay; 2. Differential algebra and generalizations of Grothendieck's conjecture on the arithmetic of linear differential equations Anand Pillay; 3. Schanuel's conjecture for non-isoconstant elliptic curves over function fields Daniel Bertrand; 4. An afterthought on the generalized Mordell-Lang conjecture Damian Rössler; 5. On the definitions of Difference Galois Groups Zoé Chatzidakis, Charlotte Hardouin and Michael F. Singer; 6. Differentially valued fields are not differentially closed Thomas Scanlon; 7. Complex analytic geometry in a nonstandard setting Ya'acov Peterzil and Sergei Starchenko; 8. Model theory and Kähler geometry Rahim Moosa and Anand Pillay; 9. Some local definability theory for holomorphic functions A. J. Wilkie; 10. Some observations about the real and imaginary parts of complex Pfaffian functions Angus Macintyre; 11. Fusion of structures of finite Morley rank Martin Ziegler; 12.Establishing the o-minimality for expansions of the real field Jean-Philippe Rolin; 13. On the tomography theorem by P. Schapira Sergei Starchenko; 14. A class of quantum Zariski geometries Boris Zilber; 15. Model theory guidance in number theory? Ivan Fesenko. Contributors |
||||||||||||||||||||||||||||
|
Anand Pillay, Daniel Bertrand, Damian Rössler, Zoé Chatzidakis, Charlotte Hardouin, Michael F. Singer, Thomas Scanlon, Ya'acov Peterzil, Sergei Starchenko, Rahim Moosa, A. J. Wilkie, Angus Macintyre, Martin Ziegler, Jean-Philippe Rolin, Boris Zilber, Ivan Fesenko |
||||||||||||||||||||||||||||
