Topics in Foundations of Math

Catalog description

Possible topics may include formal logic, naive set theory, Russell's paradox, sets and classes, transfinite ordinals and cardinals, the real number system, well-ordering and Zorn's lemma, other systems of set theory, relative consistency proofs, consistency of the axiom of choice and the generalized continuum hypothesis, Boolean logics, truth functions, quantification theory, Godel's completeness, 56 theorem, Turing machines, recursive functions, unsolvable decision problems, word problems, Post normal systems, Hilbert's tenth problem, incompleteness theorems, computable functionals, degrees of recursive insolvability. Prerequisite(s): graduate standing or permission of department.