Series: Penn State Logic Seminar Date: Tuesday, April 13, 2004 Time: 2:30 - 3:45 PM Place: 307 Boucke Building Speaker: Rebecca Weber, Mathematics, Notre Dame Title: Orbits and Invariance in the Lattice of $\Pi^0_1$ Classes Abstract: We present a definable quotient substructure of $\mathcal{E}_\Pi$, the lattice of $\Pi^0_1$ classes, and show that structure is isomorphic to $\mathcal{E}^*$, the lattice of c.e.\ sets modulo finite difference. We then explore how to use that isomorphism to transfer information from $\mathcal{E}^*$ to $\mathcal{E}_\Pi$, especially about orbits and invariant classes.