Education, Master Class, Topics 1998/1999

Master Class 1998/1999


Mathematical logic

The seventh edition of the Master Class concentrates on mathematical logic. Logic takes the language and methods of reasoning and computing in mathematics as object of study. Some branches of logic have reached a level of complexity comparable to mathematics itself and have applications in other mathematical areas. These have long been incorporated in ordinary mathematics. Other branches of logic have as goal to find formal systems in which mathematics can be conveniently carried out. An application of these branches is interactive proof-development and automated proof-checking.

The 1998/99 Master Class programme in mathematical logic aims to introduce students to some of the areas in logic which are part of the MRI research programme. The applicants are expected to be familiar with first order predicate logic (including the completeness theorem), but no further acquaintance with logic is required. In the first semester, basic courses will be taught in some of the classical cornerstone subjects, while the 'logic panorama' will introduce the student to the many varieties of logical research. In the second semester, the students will receive a thorough training in several of the topics on which research at the MRI is focussed, such as new applications to the semantics of lambda calculus and lineair logic, relations between geometry and logic, sheaf semantics and advanced lambda calculus. The lambda calculus, especially in combination with type systems, recently obtained a central role in logic and computer science by providing an integrated foundation for proving and computing. Important applications are proof development systems and functional programming languages.

Organized by I. Moerdijk and H. Barendregt

1st semester

Model theory (W. Veldman)
Lambda calculus (H. Barendregt, E. Barendsen)
Recursion theory & Proof theory (H. Schellinx)
Seminar: Logic panorama

2nd semester

Type theory and applications (H. Barendregt, E. Barendsen)
Incompleteness theorems (J. van Oosten)
Sheaves and logic (I. Moerdijk)
Seminar: Mathematical logic

Course content