[1]Aczel, P., An introduction to inductive definitions, Handbook of mathematical logic (Barwise, J., editor), North-Holland, Amsterdam, 1977, pp. 739–782.

[2]Barwise, J. and Fischer, E., The Shoenfield absoluteness lemma, Israel Journal of Mathematics, vol. 8 (1970), pp. 329–339.

[3]Beeson, M., Foundations of constructive mathematics, Springer-Verlag, Berlin, 1985.

[4]Buchholz, W., Feferman, S., Pohlers, W., and Sieg, W., Iterated inductive definitions and subsystems of analysis, Lecture Notes in Mathematics, no. 897, Springer-Verlag, Berlin, 1981.

[5]Cantini, A., On the relation between choice and comprehension principles in second order arithmetic, this Journal, vol. 51 (1986), pp. 360–373.

[6]Feferman, S., A language and axioms for explicit mathematics, Algebra and logic (Crossley, J. N., editor), Lecture Notes in Mathematics, no. 450, Springer-Verlag, Berlin, 1975, pp. 87–139.

[7]Feferman, S., Constructive theories of functions and classes, Logic colloquium '78 (Boffa, M., van Dalen, D., and McAloon, K., editors), North-Holland, Amsterdam, 1979, pp. 159–224.

[8]Feferman, S., Monotone inductive definitions, The L. E. J. Brouwer centenary symposium (Troelstra, A. S. and van Dalen, D., editors), North-Holland, Amsterdam, 1982, pp. 77–89.

[9]Feferman, S. and Sieg, W., Proof-theoretic equivalences between classical and constructive theories of analysis, Iterated inductive definitions and subsystems of analysis (Buchholz, W., Feferman, S., Pohlers, W., and Sieg, W., editors), Lecture Notes in Mathematics, no. 897, Springer-Verlag, Berlin, 1981, pp. 78–142.

[10]Friedman, H., Iterated inductive definitions and – AC, Intuitionism and proof theory (Kino, A., Myhill, J., and Vesley, R. E., editors), North-Holland, Amsterdam, 1968, pp. 435–442. [11]Glass, T., Standardstrukturen für Systeme Expliziter Mathematik, **Inaugural-Dissertation**, Münster, 1993.

[12]Glass, T., Rathjen, M., and Schlüter, A., The strength of monotone inductive definitions in explicit mathematics, Annals of Pure and Applied Logic, vol. 85 (1997), pp. 1–46.

[13]Harrington, L. A., *Kolmogorov's R-operator and the first nonprojectible ordinal*, 13 pages, mimeographed notes, 1975.

[14]Hinman, P. G., Recursion-theoretic hierarchies, Springer, Berlin, 1978.

[15]John, T., Recursion in Kolmogorov's R-operator and the ordinal σ_{3}, this Journal, vol. 51 (1986), pp. 1–11.

[16]Kechris, A. S., Spector second order classes and reflection, Generalized recursion theory II (Fenstad, J. E., Gandy, R. O., and Sacks, G. E., editors), North-Holland, Amsterdam, 1978, pp. 147–183.

[17]Kechris, A. S. and Moschovakis, Y. N., Recursion in higher types, Handbook of mathematical logic (Barwise, J., editor), North-Holland, Amsterdam, 1977, pp. 681–737.

[18]Moschovakis, Y. N., Elementary inductions on abstract structures, North–Holland, Amsterdam, 1974.

[19]Rathjen, M., *Explicit mathematics with the monotone fixed point principle, II: Models*, 33 pages, submitted.

[20]Rathjen, M., Monotone inductive definitions in explicit mathematics, this Journal, vol. 61 (1996), pp. 125–146.

[21]Richter, W. and Aczel, P., Inductive definitions and reflecting properties of admissible ordinals, Generalized recursion theory (Fenstad, J. E. and Hinman, P. G., editors), North-Holland, Amsterdam, 1974, pp. 301–381.

[22]Rogers, H., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.

[23]Schütte, K., Proof theory, Springer-Verlag, Berlin, 1977.

[24]Schwichtenberg, H., Proof theory: Some applications of cut-elimination, Handbook of mathematical logic (Barwise, J., editor), North-Holland, Amsterdam, 1977, pp. 867–895.

[25]Shoenfield, J. R., Mathematical logic, Addison-Wesley, 1967.

[26]Tait, W., Normal derivability in classical logic, The syntax and semantics of infinitary languages (Barwise, J., editor), Lectures Notes in Mathematics, no. 72, Springer-Verlag, Berlin, 1968, pp. 204–236.

[27]Takahashi, S., Monotone inductive definitions in a constructive theory of functions and classes, Annals of Pure and Applied Logic, vol. 42 (1989), pp. 255–279.