## Carl Mummert: How hard is it to find a connected component of a graph?

The next Dartmouth Logic Seminar will be on Wednesday, May 21, at 3pm in Kemeny 120.

Title: How hard is it to find a connected component of a graph?

Speaker: Carl Mummert (Marshall University)

Abstract: I will talk about recent work with Kirill Gura and Jeff Hirst on the reverse mathematics of graph theory inspired by the problem of finding a single connected component of a graph. We analyze this and related problems from the viewpoints of computability, reverse mathematics, and Weihrauch reducibility.

## Seth Harris: Graph colorings with and without weak König’s lemma

The next Dartmouth Logic Seminar will be on Tuesday, May 6, at 4pm in Kemeny 120.

Title: Graph colorings with and without weak König’s lemma

Speaker: Seth Harris (Dartmouth)

## Marcia Groszek: More on the Strength of Ramsey’s Theorem for Pairs

The next Dartmouth Logic Seminar this Winter will be on Wednesday, March 6, at 3:00pm in Kemeny 120. The speaker will be Marcia Groszek (Dartmouth College).

Title: More on the Strength of Ramsey’s Theorem for Pairs

Abstract: We will finish the forcing argument in Seetapun and Slaman 1995 showing that Ramsey’s theorem for pairs is weaker than arithmetic comprehension, and look at the complications involved in trying to do a similar argument for the binary tree version.

## Seth Harris: Ramsey’s Theorem for Trees: Notions of Stability and their Reverse Mathematics

The next Dartmouth Logic Seminar this Winter will be on Wednesday, February 27, at 3:00pm in Kemeny 120. The speaker will be Seth Harris (Dartmouth College), who will speak on Ramsey’s Theorem for Trees: Notions of Stability and their Reverse Mathematics.

## Marcia Groszek: The Strength of Ramsey’s Theorem for Pairs

The next Dartmouth Logic Seminar this Winter will be on Wednesday, February 20, at 3:00pm in Kemeny 120. The speaker will be Marcia Groszek (Dartmouth College).

Title: The Strength of Ramsey’s Theorem for Pairs

Abstract: We will review the forcing argument in Seetapun and Slaman 1995 showing that Ramsey’s theorem for pairs is weaker than arithmetic comprehension.  We may look at the complications involved in trying to do a similar argument for the binary tree version.

## François G. Dorais: The Set-Theoretic Multiverse

The Dartmouth Logic Seminar will meet on Wednesday, January 23, at 3:00pm in Kemeny 120. The speaker this week will be François G. Dorais (Dartmouth College).

Title: The Set-Theoretic Multiverse

Abstract: Joel David Hamkins proposed a list of axioms for the multiverse view of set theory. We will look at these axioms and their consequences to our understanding of the mathematical universe. We will also look at a consistency proof of the multiverse axioms by Victoria Gitman and Joel David Hamkins.

## 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.

## 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.