Global properties of the lattice of Π⁰₁ classes
Douglas Cenzer, André Nies · Proceedings of the American Mathematical Society · 2003
Let E Π \mathcal {E}_\Pi be the lattice of Π 1 0 \Pi ^0_1 classes of reals. We show there are exactly two possible isomorphism types of end intervals, [ P , 2 ω ] [P,2^\omega ] . Moreover, finiteness is first order definable in E Π \mathcal {E}_\Pi .