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Invariance in and
Authors:Rebecca Weber
Affiliation:Department of Mathematics, 255 Hurley Hall, University of Notre Dame, Notre Dame, Indiana 46556
Abstract:We define $ G$, a substructure of $ mathcal{E}_Pi$ (the lattice of $ Pi^0_1$ classes), and show that a quotient structure of $ G$, $ G^diamondsuit$, is isomorphic to $ mathcal{E}^*$. The result builds on the $ Delta^0_3$ isomorphism machinery, and allows us to transfer invariant classes from $ mathcal{E}^*$ to $ mathcal{E}_Pi$, though not, in general, orbits. Further properties of $ G^diamondsuit$ and ramifications of the isomorphism are explored, including degrees of equivalence classes and degree invariance.

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