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Academic Year 2000/2001

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. group theory, Hilbert's Nullstellensatz, Chevalley's theorem on constructible sets, and Steinitz' classification theorem for algebraically closed fields.

MAJOR READINGS

EXAMINATIONS AND ASSIGNMENTS

ADDITIONAL REQUIREMENTS and/or COMMENTS

COURSE FORMAT: Lecture

REGISTRATION INFORMATION

Level: GRAD    Credit: 1    Gen Ed Area Dept: NONE    Grading Mode: Graded   

Prerequisites: (MATH503 AND MATH504)

SECTION 01

Instructor(s): Rothmaler,Philipp S.   

Times: .M.W... 02:40PM-04:00PM;     Location: SCIE638

Reserved Seats:    (Total Limit: 15)

SR. major: 3   Jr. major: 2

SR. non-major: X   Jr. non-major: X   SO: X   FR: X

Special Attributes:

Last Updated on MAR-26-2001

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