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Dartmouth Logic
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Logic and Foundations of Mathematics at Dartmouth College
Logic and Foundations of Mathematics at Dartmouth College

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The next Dartmouth Logic Seminar this Winter will be on Wednesday, March 6, at 2:00pm 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.

The next 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.

The first seminar of Winter 2013 will be on January 23 at 3:00pm in Kemeny 120.

Title: The Set-Theoretic Multiverse
Speaker: +François Dorais (Dartmouth College)

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.

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.
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