Vol. 29, No. 2, 1969

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Initial segments of one-one degrees

Alistair H. Lachlan

Vol. 29 (1969), No. 2, 351–366

Let 0 be the one-one degree consisting of the infinite recursive sets whose complements are also infinite. In this paper are studied initial segments of the one-one degrees 0. A characterization is stated of the order types of those initial segments with greatest member which are at the same time initial segments of the many-one degrees. It is shown that any finite initial segment with greatest member is a lattice, and that any finite recursively enumerable initial segment with greatest member is a distributive lattice.

Mathematical Subject Classification
Primary: 02.70
Received: 30 August 1967
Published: 1 May 1969
Alistair H. Lachlan