I would like to know what areas of mathematic are directly related to mathematical logic, besides the usual courses on model theory, proof theory and computability. If you suggest only one book on each subject that will be great. I prefer the books to be formal, concise and to the point( Rudin style).
- Combinatorics and graph theory: Does a logic student need to know anything about enumeration? If so to what extent.
- Algebraic geometry: I know model theory has been applied to solve some problems in algebraic geometry, but is there any application of AB in logic? Or it only can serve as a source of inspiration?
- Number theory: Is knowing elementary number theory sufficient?
- Toposes and sheaves: I don't know anything about sheaves and toposes. I only know some basic category theory. I know they are important for further studies in logic but they appear in different areas of math, i.e. algebraic topology , algebraic geometry and geometry. What is the best approach to learn about them?
- Geometry: I've had some courses in differential geometry and theory of manifolds. But they don't seem to be related. Maybe synthetic geometry would've been a more suitable course to take.
- Algebra(not algebraic logic ) : Paul Cohen, a logician, if I'm not mistaken have some theorems in algebra. Why!? how are logic and algebra related? Thanks for your patience!