Splitting theorems and the jump operator

&
Annals of Pure and Applied Logic 94 (1-3):45-52 (1998)
  Copy   BIBTEX

Abstract

We investigate the relationship of the degrees of splittings of a computably enumerable set and the degree of the set. We prove that there is a high computably enumerable set whose only proper splittings are low 2

Categories

Keywords

Reprint years

DOI

10.1016/s0168-0072(97)00066-3

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Jump Theorems for REA Operators.Alistair H. Lachlan & Xiaoding Yi - 1993 - Mathematical Logic Quarterly 39 (1):1-6.
Isolation and the Jump Operator.Guohua Wu - 2001 - Mathematical Logic Quarterly 47 (4):525-534.
Jump inversions inside effectively closed sets and applications to randomness.George Barmpalias, Rod Downey & Keng Meng Ng - 2011 - Journal of Symbolic Logic 76 (2):491 - 518.
A non-inversion theorem for the jump operator.Richard A. Shore - 1988 - Annals of Pure and Applied Logic 40 (3):277-303.
Antibasis theorems for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^0_1}$$\end{document} classes and the jump hierarchy. [REVIEW]Ahmet Çevik - 2013 - Archive for Mathematical Logic 52 (1-2):137-142.
Highness and bounding minimal pairs.Rodney G. Downey, Steffen Lempp & Richard A. Shore - 1993 - Mathematical Logic Quarterly 39 (1):475-491.
Splitting theorems in recursion theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.
A jump operator on honest subrecursive degrees.Lars Kristiansen - 1998 - Archive for Mathematical Logic 37 (2):105-125.
Representing any-time and program-iteration by infinitary conjunction.Norihiro Kamide - 2013 - Journal of Applied Non-Classical Logics 23 (3):284 - 298.
Eventually infinite time Turing machine degrees: Infinite time decidable reals.P. D. Welch - 2000 - Journal of Symbolic Logic 65 (3):1193-1203.
Discontinuities of provably correct operators on the provably recursive real numbers.William J. Collins & Paul Young - 1983 - Journal of Symbolic Logic 48 (4):913-920.
Ray-Splitting Billiards.R. Blümel, P. M. Koch & L. Sirko - 2001 - Foundations of Physics 31 (2):269-281.
Analytic countably splitting families.Otmar Spinas - 2004 - Journal of Symbolic Logic 69 (1):101-117.
A jump inversion theorem for the enumeration jump.I. N. Soskov - 2000 - Archive for Mathematical Logic 39 (6):417-437.
A Jump Operator in Set Recursion.Dag Normann - 1979 - Mathematical Logic Quarterly 25 (13‐18):251-264.

Analytics

Added to PP
2014-01-16

Downloads
18 (#814,090)

6 months
7 (#418,426)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Quasi-complements of the cappable degrees.Guohua Wu - 2004 - Mathematical Logic Quarterly 50 (2):189.

Add more citations

References found in this work

Splitting theorems in recursion theory.Rod Downey & Michael Stob - 1993 - Annals of Pure and Applied Logic 65 (1):1-106.
Anti‐Mitotic Recursively Enumerable Sets.Klaus Ambos-Spies - 1985 - Mathematical Logic Quarterly 31 (29-30):461-477.
Completely mitotic R.E. degrees.R. G. Downey & T. A. Slaman - 1989 - Annals of Pure and Applied Logic 41 (2):119-152.
Anti‐Mitotic Recursively Enumerable Sets.Klaus Ambos-Spies - 1985 - Mathematical Logic Quarterly 31 (29-30):461-477.

View all 10 references / Add more references