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Model theory is the study of definability in a given formal logic--first-order (or predicate) logic in this course. Its fundamental tool is the so-called compactness theorem. In a standard logic course this theorem
would be derived from the
completeness theorem (of first-order logic). Our first objective, however, will be to give it a more algebraic proof (using ultraproducts), thus making our treatment largely independent of any such course (though
familiarity with some rudiments of mathem
atical logic is certainly helpful and welcome). A necessary prerequisite, on the other hand, is some mathematical maturity (including the acceptance of Zorn's Lemma) and algebraic culture (obtained e.g. in a course like
MATH261), for structures like vect
or spaces, groups, rings, and fields (as well as orderings) will serve as main examples throughout the course.
Depending on time and background of the audience, we may derive from our general theory such classical
algebraic results like Malcev's lo
cal theorems of group theory, Hilbert's Nullstellensatz, Chevalley's theorem on constructible sets, and Steinitz' classification theorem for algebraically closed fields.
COURSE FORMAT: Lecture
Level: GRAD Credit: 1 Gen Ed Area Dept: NONE Grading Mode: Graded
Prerequisites: NONE Links to Web Resources For This Course.
Last Updated on MAR-19-2002
Copyright Wesleyan University, Middletown, Connecticut, 06459