Journal of Symbolic Logic

Contiguity and Distributivity in the Enumerable Turing Degrees

Abstract

We prove that a (recursively) enumerable degree is contiguous iff it is locally distributive. This settles a twenty-year old question going back to Ladner and Sasso. We also prove that strong contiguity and contiguity coincide, settling a question of the first author, and prove that no $m$-topped degree is contiguous, settling a question of the first author and Carl Jockusch [11]. Finally, we prove some results concerning local distributivity and relativized weak truth table reducibility.

Article information

Source
J. Symbolic Logic, Volume 62, Issue 4 (1997), 1215-1240.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745378

Mathematical Reviews number (MathSciNet)
MR1617965

Zentralblatt MATH identifier
0897.03047

JSTOR
links.jstor.org

Citation

Downey, Rodney G.; Lempp, Steffen. Contiguity and Distributivity in the Enumerable Turing Degrees. J. Symbolic Logic 62 (1997), no. 4, 1215--1240. https://projecteuclid.org/euclid.jsl/1183745378