Information for prospective research students
My primary research interest is computability and
Some particular problems I am currently working on
- Turing definability in the local Turing
- structures and hierarchies of the Turing and
the enumeration degrees,
- elementary differences among structures of
the Turing degrees,
- enumeration operators
- automorphism of the Turing degrees,
- computable approximations
- Computability Theory
- Computational Complexity
My curriculum vitae and bibliography
Strong decomposition theorem of the recursively
enumerable degrees (in Chinese), Acta Math. Sinica, 1992, 35(2):251.
A decomposition theorem of 0', Science in China,
No.10, 1992 (in Chinese) and No.6, 1993.
A result about the pseudo jump operators, Bull. of
Chinese Sciences, No. 21, 1992.
Cupping the recursively enumerable degrees by d.r.e.
degrees (with X.Yi), Proceedings of the London Mathematical Society,
3, 78, 1999, 1-21.
A high diamond theorem, (with D. Yang), Journal of
Software, 2000, 11(1):23--39.
A hierarchy for cuppable degrees, Illinois Journal of
Mathematics, Vol. 44, No.3, 2000, 619--632. (with Wu and Zhang).
Bounding cappable degrees, Archive for Mathematical
Logic, 2000, 39:311--352.
On a Conjecture of Lempp, Archive for Mathematical
Logic, 2000, 39:281--309.
There is no low maximal d.c.e. degrees, Math. Log.
Quart. 46, 2000, 3, 409--416. (with Arslanov and Cooper).
On the distribution of Lachlan nonsplitting bases,
Archive for Math. Logic, 41, 455--482, 2002. (with Cooper and Yi).
Non-uniformity and generalised Sacks splitting, Acta
Math. Sinica, 2002. (with Cooper).
Splitting and Nonsplitting II: A rm Low_2 Computably
Enumerable Degrees Above Which 0' Is Not Splittable, Journal of
Symbolic Logic, 67(4): 1391-1430, 2002. (with S. B. Cooper).
Turing definability in the Ershov hierarchy, Journal
of the London Mathematical Society, 2(66), 513-528, 2002. (with
There exists a maximal 3-c.e. enumeration degree,
Israel Journal of Mathematics, 137 (2003), 285--320. (with S. Barry
Cooper, A. Sorbi, and Y. Yang).
A hierarchy for the plus cupping Turing degrees,
Journal of Symbolic Logic, Vo. 68, No. 3, Sept. 2003, 972--988.
(with Y. Wang).
A minimal pair joining to a plus cupping Turing
degree, Mathematical Logic Quarterly, 49, No. 6, 553--566 (2003).
(with D. Li).
The plus cupping Turing degrees do not form an ideal,
Science in China, to appear. (with Y. Zhao).
Complementing cappable degrees in the different
hierarchy, Annals of Pure and Applied Logic, 125 (2004), 101--118.
(with Guohua Wu and Rod Downey).
A join theorem for the computably enumerable degrees,
Trans. Amer. Math. Soc. 356 (2004), 2557--2568. (with Carl Jockusch
and Y. Yang)
On Lachlan's major subdegree problem. (with Cooper).
A hierarchy characterization for the cuppable
Elementary differences among jump hierarchies.
Low Splitting Theorem in the Difference Hierarchy.
RESTRICTED JUMP INTERPOLATION IN THE D.C.E. DEGREES, (with Carl G.
Jockusch, Jr. )
ON LACHLAN'S MAJOR SUB-DEGREE PROBLEM, (with S. Barry Cooper)
Computability Theory (in Chinese, with D. Yang),
Science Press, Beijing, 1999.
Definable relations on the computably enumerable
degrees, in Computability and Models (eds. Cooper and Goncharov),
Kluwer Academic/Plenum, Jan. 2003, 267--288.
Definability in local degree structure -- a survey on
recent results related to jump classes. (with Yue Yang). in
Proceedings of the 7th, and the 8th Asian Logic Conferences. World
Scientific Press, eds. R. Downey, D. Ding, S. P. Tung, Y. Qui, M.
Yasugi, 2003, 270--302.
- One hour, International Conference on Math.
Logic and Applications dedicated to A. I. Mal'tsev and the 275th
Anniversary of the Russian Academy of Sciences, Novosibirsk, Aug.
- 45 minutes, International Conference on
Mathematical Logic-- Satellite Conference of ICM Beijing 2002, and
the 8th Asian Logic Conference, Chongqing, Aug. 28--Sept. 3, 2002.
- 15 minutes, Structural Theory of the
Computably Enumerable Turing Degrees,ICM 2002, Beijing, 20--28, Aug.
- Dengfeng Li, On the relationship between the
nonbounding and the plus cupping Turing degrees. (2003)
- Yong Wang, A hierarchy for the plus
cupping Turing degrees. (2003)
- Yicheng Zhao, Algebraic structure of the
plus cupping Turing degrees. (2003)
Prepared by Angsheng Li (firstname.lastname@example.org)