Instructor: Thomas Hofweber. This course meets TR 9:30 – 10:45 a.m. in CW 213.
This course covers the basic concepts and techniques in the study of first order logic. We will discuss basic set theory and the distinction between different sizes of infinite sets, Cantor’s Theorem, induction and recursion, the meta-theory of propositional and first-order logic, in particular completeness and compactness, notions inexpressible in first-order logic, the Löwenheim-Skolem Theorems and the Skolem Paradox. We will end by applying the compactness theorem to construct non-standard models of the theory of natural numbers and of real numbers, with an emphasis on showing the coherence of infinitesimals, i.e. infinitely small numbers.