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: An Introduction to Priority and Injury
Description: A pervasive technique of proof within the field of computability theory is the priority argument. The technique involves separating a complex goal into infinitely many subgoals, each of which is assigned a priority. Higher priority subgoals are allowed to take actions that cause harm to lower priority subgoals (causing injury), but are not allowed to take action that would cause harm to even higher priority subgoals. In this course, we will discuss various types of priority arguments: moving markers, finite injury, infinite injury, etc. Examples will be drawn from degree theory, computable model theory, effective algebra, and elsewhere depending on the interests of the class. No background in computability theory is required. Knowledge of Math 5260 (Logic I) would be helpful but is not necessary.
Sections: Spring 2009 on Storrs Campus
|5026||1||Lecture||TuTh 2:00-3:15||MSB415||Asher Kach|