[1]Ash, C. J. and Knight, J. F., Computable structures and the hyperarithmetical hierarchy, 1st ed., Studies in Logic and the Foundations of Mathematics, vol. 144, North-Holland, Amsterdam, 2000.

[2]Chang, C. C. and Keisler, H. J., Model theory, 3rd ed., Studies in Logic and the Foundations of Mathematics, vol. 73, North-Holland, Amsterdam, 1990, [1st ed. 1973, 2nd ed. 1977].

[3]Csima, B. F., Degree spectra of prime models, this Journal, vol. 69 (2004), pp. 430–442.

[4]Csima, B. F., Harizanov, V. S., Hirschfeldt, D. R., and Soare, R. I., Bounding homogeneous models, this Journal, vol. 72 (2007), pp. 305–323.

[5]Csima, B. F., Hirschfeldt, D. R., Knight, J. F., and Soare, R. I., Bounding prime models, this Journal, vol. 69 (2004), pp. 1117–1142.

[6]Epstein, R., *Computably enumerable degrees of Vaught's models*, submitted.

[7]Goncharov, S. S., Strong constructivizability of homogeneous models, Algebra i Logika, vol. 17 (1978), pp. 363–388, 490, in Russian [translated in: **Algebra and Logic**, vol. 17 (1978), pp. 247-263].

[8]Goncharov, S. S. and Nurtazin, A. T., Constructive models of complete decidable theories. Algebra i Logika, vol. 12 (1973), pp. 125–142, 243, [translated in: **Algebra and Logic**, vol. 12 (1973), pp. 67-77].

[9]Harizanov, V. S., Pure computable model theory, Handbook of recursive mathematics (Ershov, Yu. L., Goncharov, S. S., Nerode, A., and Remmel, J. B., editors), Studies in Logic and the Foundations of Mathematics, vol. 138–139, North-Holland, Amsterdam, 1998, pp. 3–114.

[10]Harrington, L., Recursively presentable prime models, this Journal, vol. 39 (1974), pp. 305–309.

[11]Harris, K., *Bounding saturated models*, in preparation.

[12]Hirshfeldt, D. R., Computable trees, prime models, and relative decidability, Proceedings of the American Mathematical Society, vol. 134, 2006, pp. 1495–1498.

[13]Hirschfeldt, D. R., Shore, R. A., and Slaman, T. A., *The atomic model theorem*, submitted.

[14]Knight, J. F., Degrees coded in jumps of orderings, this Journal, vol. 51 (1986), pp. 1034–1042.

[15]Lange, K. M., *A characterization of the ***0**-basis homogeneous bounding degrees, in preparation.

[16]Lange, K. M., *Reverse mathematics of homogeneous models*, in preparation.

[17]Lange, K. M. and Soare, R. I., Computability of homogeneous models, Notre Dame Journal of Formal Logic, vol. 48 (2007), no. 1, pp. 143–170.

[18]Marker, D., Model theory: an introduction, Graduate Texts in Mathematics, vol. 277, New York, 2002.

[19]Millar, T. S., Foundations of recursive model theory, Annals of Mathematical Logic, vol. 13 (1978), pp. 45–72.

[20]Millar, T. S., Homogeneous models and decidability, Pacific Journal of Mathematics, vol. 91 (1980), pp. 407–418.

[21]Millar, T. S., Type structure complexity and decidability, Transactions of the American Mathematical Society, vol. 271 (1982), pp. 73–81.

[22]Morley, M., Decidable models, Israel Journal of Mathematics, vol. 25 (1976), pp. 233–240.

[23]Peretyat'kin, M. G., A criterion for strong constructivizability of a homogeneous model, Algebra i Logika, vol. 17 (1978), pp. 436–454, 491, in Russian, [translated in: **Algebra and Logic**, vol. 19 (1980), pp. 202–229].

[24]Soare, R. I., Recursively enumerable sets and degrees: A study of computable functions and computably generated sets, Springer-Verlag, Heidelberg, 1987.

[25]Soare, R. I., Computability theory and applications, Springer-Verlag, Heidelberg, in preparation.

[26]Tusupov, D. A., Numerations of homogeneous models of decidable complete theories with a computable family of types, Theory of algorithms and its applications (Remeslennikov, V. N., editor), Computable Systems, vol. 129.

[27]Vaught, R. L., Denumerable models of complete theories, Infinitistic Methods (Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 1959), Pergamon Press, 1961, pp. 301–321.