Angsheng Li    

Address:

Institute of Software, 
Chinese Academy of Sciences
P.O. Box 8718
Beijing, 100080 
P.R. CHINA

Phone/Fax/Email:

Office: 86-10-82625471
Home: 86-10-82522687
Fax: 86-10-82625471
Email: angsheng@gcl.iscas.ac.cn

 

 

Information for prospective research students 

My research interests

My primary research interest is computability and computational complexity.

Some particular problems I am currently working on include

  • Turing definability in the local Turing degrees,
  • 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

Courses

  • Computability Theory
  • Computational Complexity

My curriculum vitae and bibliography

 

Papers on line

Journal papers

  1. Strong decomposition theorem of the recursively enumerable degrees (in Chinese), Acta Math. Sinica, 1992, 35(2):251.

  2. A decomposition theorem of 0', Science in China, No.10, 1992 (in Chinese) and No.6, 1993.

  3. A result about the pseudo jump operators, Bull. of Chinese Sciences, No. 21, 1992.

  4. Cupping the recursively enumerable degrees by d.r.e. degrees (with X.Yi), Proceedings of the London Mathematical Society, 3, 78, 1999, 1-21.

  5. A high diamond theorem, (with D. Yang), Journal of Software, 2000, 11(1):23--39.

  6. A hierarchy for cuppable degrees, Illinois Journal of Mathematics, Vol. 44, No.3, 2000, 619--632. (with Wu and Zhang).

  7. Bounding cappable degrees, Archive for Mathematical Logic, 2000, 39:311--352.

  8. On a Conjecture of Lempp, Archive for Mathematical Logic, 2000, 39:281--309.

  9. There is no low maximal d.c.e. degrees, Math. Log. Quart. 46, 2000, 3, 409--416. (with Arslanov and Cooper).

  10. On the distribution of Lachlan nonsplitting bases, Archive for Math. Logic, 41, 455--482, 2002. (with Cooper and Yi).

  11. Non-uniformity and generalised Sacks splitting, Acta Math. Sinica, 2002. (with Cooper).

  12. 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).

  13. Turing definability in the Ershov hierarchy, Journal of the London Mathematical Society, 2(66), 513-528, 2002. (with Cooper)

  14. 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).

  15. A hierarchy for the plus cupping Turing degrees, Journal of Symbolic Logic, Vo. 68, No. 3, Sept. 2003, 972--988. (with Y. Wang).

  16. A minimal pair joining to a plus cupping Turing degree, Mathematical Logic Quarterly,  49, No. 6, 553--566 (2003). (with D. Li).

  17. The plus cupping Turing degrees do not form an ideal, Science in China, to appear. (with Y. Zhao).

  18. Complementing cappable degrees in the different hierarchy, Annals of Pure and Applied Logic, 125 (2004), 101--118. (with Guohua Wu and Rod Downey).

  19. A join theorem for the computably enumerable degrees, Trans. Amer. Math. Soc. 356 (2004), 2557--2568. (with Carl Jockusch and Y. Yang)

 

Preprints

  1. On Lachlan's major subdegree problem. (with Cooper).

  2. A hierarchy characterization for the cuppable degrees.

  3. Elementary differences among jump hierarchies. 

  4. Low Splitting Theorem in the Difference Hierarchy.

  5. RESTRICTED JUMP INTERPOLATION IN THE D.C.E. DEGREES, (with Carl G. Jockusch, Jr. )

  6. ON LACHLAN'S MAJOR SUB-DEGREE PROBLEM, (with S. Barry Cooper)

Books

  1. Computability Theory (in Chinese, with D. Yang), Science Press, Beijing, 1999.

Non-Journal papers

  1. Definable relations on the computably enumerable degrees, in Computability and Models (eds. Cooper and Goncharov), Kluwer Academic/Plenum, Jan. 2003, 267--288.

  2. 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.

Conference Talk

  1. 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. 10--15, 1999.
  2. 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.
  3. 15 minutes, Structural Theory of the Computably Enumerable Turing Degrees,ICM 2002, Beijing, 20--28, Aug.

 

Some theses on line

  • 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 (angsheng@gcl.iscas.ac.cn)