About this Master Class

The three basic concepts that are at the basis of Mathematical Logic (and which obtained a rigorous formulation roughly at the same time, in the twenties-thirties of the past century) are ``proof'', ``truth'' and ``computation''.
Logicians defined a formal language and gave a precise meaning to the statement that a sentence of this formal language is ``true'' in an appropriate model.
A formal ``proof'' is a structure of such sentences with a definite conclusion and premises. Godel's Completeness Theorem (the start of Logic as a scientific discipline) says that a sentence is true in every appropriate model, precisely if it is the conclusion of some proof.
Around the same time (1930), the concept of an ``algorithm'' was defined, and the question whether certain problems could be effectively solved, could be studied. A famous example is Hilbert's 10th problem: give an algorithm by which one can decide whether a given Diophantine equation has a solution in the integers. It could be shown in 1970 that such an algorithm cannot exist. Work on similar problems continues to this day.

In the second half of the twentieth century, Logic became prominent in several developments. The geometrically motivated notion of a ``topos'' turned out to have strong connections to Logic, and led to a revival of the study of Brouwer's ``intuitionism''. Another development for which Logic proved useful was the advent of Computer Science. The use of computers, not only to do calculations or to verify proofs, but even to construct proofs, has become a major research area. These are just two examples of areas in which Logic is important. In both these areas, the universities of Utrecht and Nijmegen are international centers of research.

The Master Class in Mathematical Logic aims to provide the student with a thorough introduction to the general field, as well as to introduce her/him to research, in advanced, specialized courses. The courses are all given by lecturers who are active researchers. Interaction and enthusiasm are the key words.

This Master Class is affiliated to the research cluster Diamant, supported by NWO, and is organized in collaboration with the Department of Computer Science in Nijmegen and the Department of Philosophy in Utrecht.