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Global properties of the lattice of classes

Authors:	Douglas Cenzer André Nies

Institution:	Department of Mathematics, University of Florida, Gainesville, Florida 32611 ; Department of Mathematics, The University of Chicago, 5734 S. University Ave., Chicago, Illinois 60637

Abstract:	Let $\mathcal{E}_\Pi$ be the lattice of $\Pi^0_1$ classes of reals. We show there are exactly two possible isomorphism types of end intervals, $P,2^\omega]$ . Moreover, finiteness is first order definable in $\mathcal{E}_\Pi$ .

Keywords:	$\Pi^0_1$ classes definability end segments

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