MATH 5026: Topics in Mathematical Logic
Description: Topics include, but are not restricted to, recursion theory (degree structures, hyperarithmetic hierarchy, applications to computable algebra, reverse mathematics), model theory (quantifier elimination, o-minimality, types, categoricity, indiscernible), set theory (ordinals, cardinals, Martin's axiom, constructible sets, forcing), and proof theory (deductive systems, cut elimination and applications, ordinal analysis). With a change of content, this course is repeatable to a maximum of twelve credits.
Prerequisites: MATH 5260.
MATH 5026 - Section 1: Set Theory
Description: This course is an introduction to set theory. We will start with the ZFC axioms and a development of ordinal and cardinal numbers. The heart of the course will be a study of the constructible universe (giving a model of the Generalized Continuum Hypothesis and the Axiom of Choice) and the method of Cohen forcing (giving models in which the Continuum Hypothesis and the Axiom of Choice fail). Text: We will use Set Theory: An Introduction to Independence Proofs by Ken Kunen.
Prerequisites: The prerequisite is some background in formal logic, specifically the syntax and semantics for a first order language. Math 5260 is more than sufficient. If you are interested in this course and have not taken a logic course before, please speak with me. You can fairly easily obtain the required background with a couple weeks of reading over the summer.
Sections: Fall 2014 on Storrs Campus
|15024||5026||001||Lecture||MWF 12:20 PM-1:10 PM||MSB219||Solomon, David|