CUNY Ph.D. Program in Mathematics
Spring 2019
MATH 71200 - Set Theory and Logic - Logic I
Wednesday/Friday from 12:15 to 1:45, Rm. 9116
4.5 cr.
Continuing the logic course from the previous semester, the main goal of this course is to prove Gödel's Incompleteness Theorem, which says that it cannot be decided by a finitistic algorithm whether a sentence is provable or not. In order to be able to state that theorem precisely, we shall briefly develop the basics of computability theory. All the proofs will take place in the framework of a weak set theory which will be used as the metatheory. This way, this course is intended to show how intricately model theory, computability theory, proof theory and set theory are intertwined. Time permitting, we will begin exploring the theory of large cardinals.
This is the most current version of the lecture notes for the course, in pdf format. If you find any typos, please email them to me!
Here is the syllabus.
Here are the homework problem sets for the course: