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

Logic Seminar will meet on Wednesday, September 26, at 3:00pm in Kemeny 120. The speaker this week will be François G. Dorais (Dartmouth College).

Title: Interpreting set theory in second-order arithmetic

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.

We will begin with a review of second-order arithmetic, so familiarity with $ACA_0$, $ACA_0^+$, $ATR_0$ and other subsystems of second-order arithmetic is not necessary.

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