### 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.

**Credits:** 3

### MATH 5026 - Section 1: Introduction to Randomness

**Description:** Definitions of randomness using different paradigms, and their relationships to computability theory and reverse mathematics. Topics include: Kolmogorov complexity, Martin-Löf randomness, computable and left-c.e. reals, Van Lambalgens theorem, effective 0-1 laws, Pi^0_1 classes of randoms and their properties, and the relationship of random reals to PA sets.

**Credits:** 3

**Sections: **Fall 2016 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

10602 | 5026 | 001 | Lecture | MWF 12:20:00 PM-01:10:00 PM | MONT 314 | Dzhafarov, Damir |