1 K., Ambos-Spies and A., Kučera, Randomness in computability theory, Computability theoryand its applications (Cholak, Lempp, Lerman, and Shore, editors), Contemporary Mathematics, vol. 257, 2000. pp. 1–14.Google Scholar

2 K., Ambos-Spies and E., Mayordomo, Resource bounded measure and randomness, Complexity,logic and recursion theory (A. Sorbi, editor), Marcel-Decker, New York, 1997. pp. 1–48.

3 K., Ambos-Spies, K., Weihrauch, and X., Zheng, Weakly computable real numbers, Journalof Complexity, vol. 16 (2000), no. 4, pp. 676–690.Google Scholar

4 J., Brzdin，, Complexity of programs to determine whether natural numbers not greater thann belong to a recursively enumerable set, Soviet Mathematics Doklady, vol. 9 (1968), pp. 1251–1254.Google Scholar

5 O., Belegradek, On algebraically closed groups, Algebra i Logika, vol. 13 (1974), no. 3, pp. 813–816.Google Scholar

6 C., Calude, Information theory and randomness, an algorithmic perspective, Springer-Verlag, Berlin, 1994.

7 C., Calude, R., Coles, P., Hertling, and B., Khoussainov, Degree-theoretic aspects ofcomputably enumerable reals, Models and computability (Cooper and Truss, editors), Cambridge University Press, 1999.

8 C., Calude, P., Hertling, B., Khoussainov, and Y., Wang, Recursively enumerable realsand Chaitin's number, Stacs ‘98, Springer Lecture Notes in Computer Science, vol. 1373, 1998. pp. 596–606.Google Scholar

9 C., Calude and A., Nies, Chaitin's Ω numbers and strong reducibilities, Journal of UniversalComputer Science, vol. 3 (1997), pp. 1162–1166.Google Scholar

10 G., Chaitin, A theory of program size formally identical to information theory, Journal ofthe Association for Computing Machinery, vol. 22 (1975), pp. 329–340.Google Scholar

11 G., Chaitin, Information-theoretical characterizations of recursive infinite strings, TheoreticalComputer Science, vol. 2 (1976), pp. 45–48.Google Scholar

12 R., Downey, Computability, definability, and algebraic structures, to appear, Proceedings of the 7th Asian Logic Conference, Taiwan.

13 R., Downey, On the universal splitting property, Mathematical Logic Quarterly, vol. 43 (1997), pp. 311–320.Google Scholar

14 R., Downey, Some recent progress in algorithmic randomness, Proceedings,Mathematical Foundationsof Computer Science, 2004.

15 R., Downey,D.Ding, S.P., Tung, Y.H., Qiu, M.Yasuugi, andG.Wu (editors), Proceedingsof the 7th and 8th Asian logic conferences, World Scientific, 2003.

16 R., Downey and E., Griffiths, On Schnorr randomness, The Journal of Symbolic Logic, vol. 62 (2004), pp. 533–554.Google Scholar

17 R., Downey, E., Griffiths, and D., Hirschfeldt, Submartingale reducibility and the calibrationof randomness, in preparation.

18 R., Downey, E., Griffiths, and S., Reid, Kurtz randomness, Theoretical Computer Science, (to appear).

19 R., Downey and D., Hirschfeldt, Walter De Gruyter, Berlin and New York, 2001. (Short courses in complexity from the New Zealand Mathematical Research Institute summer 2000 meeting, Kaikoura).

20 R., Downey and D., Hirschfeldt, Algorithmic randomness and complexity, Monographs in Computer Science, Springer-Verlag, to appear.

21 R., Downey, D., Hirschfeldt, and G., Laforte, Undecidability of Solovay and other degreestructures for c.e., reals, in preparation.

22 R., Downey, D., Hirschfeldt, and G., Laforte, Randomness and reducibility, Journal of Computing and System Sciences, vol. 68 (2004), pp. 96–114, extended abstract in the Proceedings of Mathematical Foundations of ComputerScience 2001, (J. Sgall, A., Pultr, and P., Kolman, editors), Lecture Notes in Computer Science 2136, Springer, 2001. pp. 316–327.

23 R., Downey, D., Hirschfeldt, and A., Nies, Randomness, computability and density, SIAM Journal on Computing, vol. 31 (2002), pp. 1169–1183, (Extended abstract in STACS'01).Google Scholar

24 R., Downey, D., Hirschfeldt, A., Nies, and F., Stephan, Trivial reals, Proceedings ofthe 7th and 8th Asian logic conferences (R., Downey, D., Ding, S., Tung, Y., Qiu, and M., Yasugi, editors), World Scientific, 2003. pp. 103–131.Google Scholar

25 R., Downey, D., Hirschfeldt, A., Nies, and S., Terwijn, Calibrating randomness, TheBulletin of Symbolic Logic, (to appear).

26 R., Downey, C., Jockusch, and M., Stob, Array nonrecursive sets and multiple permittingarguments, Recursion theory week (Ambos-Spies, Muller, and Sacks, editors), Lecture Notes in Mathematics, vol. 1432, 1990. pp. 141–174.Google Scholar

27 R., Downey and G., LaForte, Presentations of computably enumerable reals, TheoreticalComputer Science, (to appear).

28 R., Downey and M., Stob, Splitting theorems in recursion theory, Annals of Pure andApplied Logic, vol. 65 (1993), no. 1, pp. 1–106.Google Scholar

29 R., Downey and S., Terwijn, Presentations of computably enumerable reals and ideals, Mathematical Logic Quarterly, vol. 48 (2002), no. 1, pp. 29–40.Google Scholar

30 R.G., Downey, G., Laforte, and A., Nies, Enumerable sets and quasi-reducibility, Annalsof Pure and Applied Logic, vol. 95 (1998), pp. 1–35.Google Scholar

31 R.G., Downey and J.B., Remmel, Classification of degree classes associated with r.e.subspaces, Annals of Pure and Applied Logic, vol. 42 (1989), pp. 105–125.Google Scholar

32 L., Fortnow, Kolmogorov complexity, in [19], pp. 73–86.

33 D., Hirschfeldt, personal communication, February 2001.

34 Chun-Kuen, Ho, Relatively recursive reals and real functions, Theoretical Computer Science, vol. 219 (1999), pp. 99–120.Google Scholar

35 S., Ishmukhametov, Weak recursive degrees and a problem of Spector, Recursion theoryand complexity (Arslanov and Lempp, editors), de Gruyter, Berlin, 1999. pp. 81–88.

36 C.G., Jockusch Jr., Fine degrees of word problems in cancellation semigroups, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 26 (1980), pp. 93–95.Google Scholar

37 Ker-I, Ko Degrees of random sets, Ph.D. thesis, Cornell, 1991.

38 Ker-I, Ko, On the continued fraction representation of computable real numbers, TheoreticalComputer Science, A, vol. 47 (1986), pp. 299–313.Google Scholar

39 Ker-I, Ko, Complexity of real functions, Birkhäuser, Berlin, 1991.

40 Ker-I, Ko and H., Friedman, On the computational complexity of real functions, TheoreticalComputer Science, vol. 20 (1982), pp. 323–352.Google Scholar

41 A., Kučera, On the use of diagonally nonrecursive functions, Logic colloquium, ‘87 (Amsterdam), North-Holland, 1989. pp. 219–239.

42 A., Kučera, On relative randomness, Annals of Pure and Applied Logic, vol. 63 (1993), pp. 61–67.Google Scholar

43 A., Kučera and T., Slaman, Randomness and recursive enumerability, SIAM Journal onComputing, vol. 31 (2001), pp. 199–211.Google Scholar

44 A., Kučera and S., Terwijn, Lowness for the class of random sets, The Journal of SymbolicLogic, vol. 64 (1999), pp. 1396–1402.Google Scholar

45 M., Kummer, Kolmogorov complexity and instance complexity of recursively enumerablesets, SIAM Journal on Computing, vol. 25 (1996), pp. 1123–1143.Google Scholar

46 S., Kurtz, Randomness and genericity in the degrees of unsolvability, Ph.D thesis, University of Illinois at Urbana.

47 L., Levin, Measures of complexity of finite objects (axiomatic description), Soviet MathematicsDolkady, vol. 17 (1976), pp. 552–526.Google Scholar

48 Ming, Li and P., Vitanyi, Kolmogorov complexity and its applications, Springer-Verlag, 1993.

49 D., Loveland, Avariant of the Kolmogorov concept of complexity, Information and Control, vol. 15 (1969), pp. 510–526.Google Scholar

50 A., Macintyre, Omitting quantifier free types in generic structures, The Journal of SymbolicLogic, vol. 37 (1972), pp. 512–520.Google Scholar

51 P., Martin-Löf, The definition of random sequences, Information and Control, vol. 9 (1966), pp. 602–619.Google Scholar

52 M., Pour-El, From axiomatics to intrinsic characterization, some open problems in computableanalysis, Theoretical Computer Science, A, (to appear).

53 M., Pour-El and I., Richards, Computability in analysis and physics, Springer-Verlag, Berlin, 1989.

54 J., Rasonnier, A mathematical proof of S. Shelah's theorem on the measure problem andrelated results, Israel Journal of Mathematics, vol. 48 (1984), pp. 48–56.Google Scholar

55 H., Rice, Recursive real numbers, Proceedings of the American Mathematical Society, vol. 5 (1954), pp. 784–791.Google Scholar

56 C.P., Schnorr, A unified approach to the definition of a random sequence, MathematicalSystems Theory, vol. 5 (1971), pp. 246–258.Google Scholar

57 R., Soare, Cohesive sets and recursively enumerable Dedekind cuts, Pacific Journal ofMathematics, vol. 31 (1969), no. 1, pp. 215–231.Google Scholar

58 R., Soare, Recursion theory and Dedekind cuts, Transactions of the American MathematicalSociety, vol. 140 (1969), pp. 271–294.Google Scholar

59 R., Soare, Recursively enumerable sets and degrees, Springer, Berlin, 1987.

60 R., Solomonoff, A formal theory of inductive inference, part 1 and part 2, Information andControl, vol. 7 (1964), pp. 224–254.Google Scholar

61 R., Solovay, Draft of paper (or series of papers) on Chaitin's work, unpublished notes, May 1975, 215.pages.

62 F., Stephan, personal communication.

63 S., Terwijn and D., Zambella, Algorithmic randomness and lowness, The Journal of SymbolicLogic, vol. 66 (2001), pp. 1199–1205.Google Scholar

64 A., Turing, On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, vol. 42 (1936), pp. 230–265, correction in Proceedings of the London Mathematical Society, 43.(1937), 544–546.Google Scholar

65 M., van Lambalgen, Random sequences, Ph.D thesis, University of Amsterdam, 1987.

66 K., Weihrauch, Computability, Springer-Verlag, Berlin, 1987.

67 K., Weihrauch and X., Zheng, Arithmetical hierarchy of real numbers, Mathematicalfoundations of computer science 1999 (Sklarska Poreba, Poland), September 1999, pp. 23–33.

68 Gouhua, Wu, Presentations of computable enumerable reals and the initial segment ofcomputable enumerable degrees, Proceedings of COCOON' 01, Guilin, China, 2001.

69 M., Ziegler, Algebraisch abgeschlossene Gruppen, Word problems II, the Oxford book (Adian, Boone, and Higman, editors), North-Holland, 1980. pp. 449–576.