Vol. 29, No. 2, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1  2
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Initial segments of one-one degrees

Alistair H. Lachlan

Vol. 29 (1969), No. 2, 351–366
Abstract

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
Milestones
Received: 30 August 1967
Published: 1 May 1969
Authors
Alistair H. Lachlan