François G. Dorais: Interpreting set theory in second-order arithmetic

Logic Seminar will meet on Wednesday, October 10, at 3:00pm in Kemeny 120. The speaker this week will be François G. Dorais (Dartmouth College), who will continue the topic from last time.

Title: Interpreting set theory in second-order arithmetic (second part)

Abstract: We will discuss the problem of interpreting fragments of set theory into subsystems of second-order arithmetic. We will see how and why $ATR_0$ is the weakest subsystem of second-order arithmetic that has a robust interpretation of set theory. We will discuss what can be done in weaker subsystems such as $ACA_0$ and $ACA_0^+$. Finally, we will discuss potential applications to reverse mathematics.