Objectives (Leerdoelen)
The student becomes familiar with some results and techniques from model theory, the most important meeting point between mathematics and mathematical logic.
|
Contents (Beschrijving)
In mathematics one often studies the class of structures satisfying a given set of formal axioms, for instance the class of groups, the class of fields, or the class of linear orders. In Model theory one starts to restrict oneself to the still rather general case that the axioms are formulated in a first-order or elementary language. This means that, when interpreting the formulas of such a language, one only quantifies over the domain of a given structure, and not, for instance, over the power set of the domain. One then asks questions like: given a structure, is it possible to axiomatize it, that is, is it possible to indicate a not too difficult set of formulas valid in the structure such that every formula valid in the structure logically follows from the formulas in the set. Or: given structures A, B, under what circumstances are A, B elementarily equivalent, that is, when do they satisfy the same elementary formulas? Or: given a set of formulas, how many countable structures do there exist satisfying all formulas in the set? Model theory at its best is a delightful blend of abstract and concrete reasoning.
|
Examination (Tentaminering)
After having completed and submitted a number of exercises, students have to pass an oral examination
|
Literature (Literatuur)
C.C. Chang, H.J. Keisler, Model Theory, North Holland Publ. Co., Amsterdam, 1977.
G.E. Sacks, Saturated Model Theory, Benjamin, Reading, Mass.,1972.
B. Poizat, Cours de théorie des Modèles, Nur al-Matiq wal-Marífah, 1985.
W. Hodges, A shorter Model Theory, Cambridge University Press, 1997.
|
