Undergraduate Mathematics Students

LOG 433/537 -- NEW COURSE SPRING 2009

NEW COURSE SPRING 2009
LOG 437/537: MODEL-THEORETIC SEMANTICS
Johannes Hafner, PhD (Berkeley)
WI 446, Email: jhafner@unity.ncsu.edu, Tel: 515 0306

This course is an introduction to the fundamental concepts and methods of model-theoretic
semantics and their applications in logic, foundations of mathematics, philosophy, and computer
science. We will prove the classical theorems of completeness and compactness of first-order logic
and introduce along the way the basic notions of structure, truth in a structure, substructure, isoand
homomorphism, elementary equivalence etc. The techniques of model construction used in
these proofs are then further refined and applied in a variety of mathematical problems. The
Löwenheim-Skolem Theorems are derived and we will examine their bearing on ontological
questions in philosophy. Further topics include the interpolation theorem; implicit definability
and its connection with circumscription in artificial intelligence; the method of elimination of
quantifiers applied, among others, to the theory of real closed fields. Finally we will complement
our treatment of model theory for first-order logic by a study of the semantics of second-order
logic and of propositional as well as quantified modal logic.

Posted at 04:15PM Oct 10, 2008 by scroggs in Courses and Advising  |  Comments[0]