[ Wesleyan Home Page ] [ WesMaps Home Page ] [ WesMaps Archive ] [ Course Search ] [ Course Search by CID ]
Academic Year 2001/2002


Model Theory
MATH 509 FA

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.

MAJOR READINGS

INTRODUCTION TO MODEL THEORY, by Philipp Rothmaler, Gordon & Breach Publ. (to appear Fall 2000)

EXAMINATIONS AND ASSIGNMENTS

Frequent problem sets and take-home final.

ADDITIONAL REQUIREMENTS and/or COMMENTS

Undergraduates wishing to attend may want to consult instructor prior to first class.

COURSE FORMAT: Lecture

REGISTRATION INFORMATION

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


Contact wesmaps@wesleyan.edu to submit comments or suggestions. Please include a url, course title, faculty name or other page reference in your email

Copyright Wesleyan University, Middletown, Connecticut, 06459