Becher, V. and Chaitin, G., Another example of higher order randomness, Fundamenta Informaticae, vol. 51 (2002), no. 4, pp. 325–338.
Becher, V., Chaitin, G., and Daicz, S., A highly random number, Proceedings of the third discrete mathematics and theoretical computer science conference (DMTCS '01) (Calude, C. S., Dineen, M. J., and Sburlan, S., editors), Springer-Verlag, 2001, pp. 55–68.
Becher, V. and Grioorieff, S., Recursion and topology on 2≤ω-m for possibly infinite computations, Theoretical Computer Science, vol. 322 (2004), pp. 85–136.
Becher, V., Random reals and possibly infinite computations, Part II: Higher order randomness, In preparation.
Becher, V., Wadge reducibility and spectral continuous maps into 2≤ω, In preparation.
Boasson, L. and Nivat, M., Adherences of languages, Journal of Computer and System Sciences, vol. 20 (1980), pp. 285–309.
Calude, C., Information and randomness, Springer, 1994.
Calude, C. S., Hertling, P. H., and Khoussainov, B.Wang, Y., Recursively enumerable reals and Chaitin Ω numbers, STACS 98 (Paris, 1998), Lecture Notes in Computer Science, no. 1373, Springer-Verlag, 1998, pp. 596–606.
Chaitin, G., A theory of program size formally identical to information theory, Journal of the ACM, vol. 22 (1975), pp. 329–340, Available on Chaitin's home page.
Chaitin, G., Algorithmic entropy of sets, Computers & Mathematics with Applications, vol. 2 (1976), pp. 233–245. Available on Chaitin's home page.
Chaitin, G., Algorithmic information theory, 1st ed., Cambridge University Press, 1987.
Downey, R., Some computability-theoretical aspects of reals and randomness, Notes from lectures given at the University Notre Dame. Available at MSCS, University of Wellington, NZ, 2000.
Downey, R. and Hirschfeldt, D., Algorithmic randomness and complexity, Springer, 2005, To appear. Preliminary version, November 30th 2004, available on Downey's home page.
Downey, R., Hirschfeldt, D., and Nies, A., Randomness, computability and density, SIAM Journal on Computing, vol. 31 (2002), pp. 1169–1183, Extended abstract in Proceedings of the STACS 2001, LNCS 2010.
Downey, R. and Laforte, G. L., Presentations of computably enumerable reals, Theoretical Computer Science, vol. 284 (2002), no. 2, pp. 539–555.
Head, T., The adherences of languages as topological spaces, Automata andinfinite words (Nivat, M. and Perrin, D., editors), Lecture Notes in Computer Science, vol. 192, 1985, pp. 147–163.
Head, T., The topological structure of adherence of regular languages, RAIRO, Theoretical Informatics and Applications, vol. 20 (1986), pp. 31–41.
Kechris, A. S., Classical descriptive set theory, Springer, 1995.
Levin, L., On the notion of random sequence, Soviet Math. Dokl., vol. 14 (1973), no. 5, pp. 1413–1416.
Li, M. and Vitanyi, P., An introduction to Kolmogorov complexity and its applications, 2d ed., Springer, 1997.
Martin-Löf, P., The definition of random sequences, Information and Control, vol. 9 (1966), pp. 602–619.
Miller, J., Personal communication.
Moschovakis, Y. N., Descriptive set theory, North Holland, 1980.
Muchnik, An. A., Personal communication.
Odifreddi, P., Classical recursion theory, Studies in Logic, vol. 125, North-Holland, 1989.
Rogers, H., Theory of recursive functions and effective computability, McGraw-Hill, 1967.
Sacks, G. E., Degrees of unsolvahility, Annals of mathematical studies, Princeton University Press, 1966.
Schnorr, C. P., Process complexity and effective random tests, Journal of Computer and System Sciences, vol. 7 (1973), pp. 376–388.
Schnorr, C. P., A survey of the theory of random sequences, Basic problems in methodology and linguistics (Butts, R. E. and Hintikka, J., editors), D. Reidel, 1977, pp. 193–210.
Soare, R., Recursion theory and Dedekind cuts, Transactions of the American Mathematical Society, vol. 140 (1969), pp. 271–294.
Solovay, R. M., Draft of a paper (or a series of papers) on Chaitin's work, Unpublished manuscript, IBM Research Center, NY, 1975.
Solovay, R. M., On random R.E. sets, Non-classical logics, model theory and computability (Arruda, A. I., da Costa, N. C. A., and Chuaqui, R., editors), North-Holland, 1977, pp. 283–307.
Turing, A., On computable numbers, with an application to the Entscheidungsproblem., Proceedings of the London Mathematical Society, 2nd series, vol. 42 (1936), pp. 230–265. Correction, A. Turing, On computable numbers, with an application to the Entscheidungsproblem., Proceedings of the London Mathematical Society, 2nd series, vol. 43 (1937) pp. 544–546.
Wadge, W. W., Degrees of complexity of subsets of the Baire space, Notices of the American Mathematical Society, (1972), pp. A–714.
Wadge, W. W., Degrees of complexity of subsets of the Baire space, Ph.D. thesis, University of Berkeley, 1984.