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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 mathematical 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 vector 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 local 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-21-2005
Copyright Wesleyan University, Middletown, Connecticut, 06459