Mathematical Logic Quarterly

Discontinuity of Cappings in the Recursively Enumerable Degrees and Strongly Nonbranching Degrees

Journal Article

Abstract

We construct an r. e. degree a which possesses a greatest a‐minimal pair b0, b1, i.e., r. e. degrees b0 and b1 such that b0, b1 < a, b0 ∩ b1 = a, and, for any other pair c0, c1 with these properties, c0 ≤ bi and c1 ≤ b1‐i for some i ≤ 1. By extending this result, we show that there are strongly nonbranching degrees which are not strongly noncappable. Finally, by introducing a new genericity concept for r. e. sets, we prove a jump theorem for the strongly nonbranching and strongly noncappable r. e. degrees.

Mathematics Subject Classification: 03D25.

Related Topics

Related Publications

Related Content

Site Footer

Address:

This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.