An Introduction to Inductive Definitions

Studies in Logic and the Foundations of Mathematics

Volumn 90, Issue C, 1977, Pages 739-782

  Aczel, Peter ^a  

^a NONE

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[No Author keywords available]

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EID: 77956968984     PISSN: 0049237X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0049-237X(08)71120-0     Document Type: Article

References (39)

1. Aanderaa, S., Inductive definitions and their closure ordinals. Fenstad, J.E., Hinman, P.G., (eds.) Generalized Recursion Theory, 1974, North-Holland, Amsterdam, 207–220.
2. Aczel, P., Representability in some systems of second order arithmetic. Israel J. Math. 8 (1970), 309–328.
3. [1973] Infinitary logic and the Barwise compactness theorem, in: Proceedings of the Bertrand Russell Logic Conference, edited by J. Bell. J. Cole. G. Priest and A. Slomson (published by the conference) pp. 234–277.
4. [1975] Quantifiers, games and inductive definitions, in: Third Scandinavian Logic Symposium, edited by S. Kanger, (North-Holland, Amsterdam) pp. 1–14.
5. P. Aczel & W. Richter [1972] Inductive definitions and analogues of large cardinals, in: Conference in Mathematical Logic—London ‘70, Lecture Notes in Mathematics, Vol. 255 (Springer, Berlin) pp. 1–9.
6. Addison, J.W., Kleene, S.C., A note on function quantification. Proc. Am. Math. Soc. 8 (1957), 1002–1006.
7. Barwise, J., Admissible sets over models of set theory. Fenstad, J.E., Hinman, P.G., (eds.) Generalized Recursion Theory, 1974, North-Holland, Amsterdam, 97–122.
8. Admissible Sets and Structures, 1975, Springer, Berlin.
9. Barwise, J., Candy, R.O., Moschovakis, Y.N., The next admissible set. J. Symbolic Logic 36 (1971), 108–120.
10. Cenzer, D., Ordinal recursion and inductive definitions. Fenstad, J.E., Hinman, P.G., (eds.) Generalized Recursion Theory, 1974, North-Holland, Amsterdam, 221–264.
11. Chang, C.C., Keisler, H.J., Model Theory, 1973, North-Holland, Amsterdam.
12. G. Ennis [1975] An extension of the next admissible set construction, mimeographed notes.
13. Feferman, S., Autonomous transfinite progressions and the extent of predicative mathematics. van Rootselaar, B., Staal, J.F., (eds.) Logic, Methodology and Philosophy of Science III, 1968, North-Holland, Amsterdam, 121–135.
14. Formal theories for transfinite iterations of generalised inductive definitions and some subsystems of analysis. Kino, A., Myhill, J., Vesley, R.E., (eds.) Intuitionism and Proof Theory, 1970, North-Holland, Amsterdam, 303–326.
15. Fenstad, J.E., Hinman, P.G., (eds.) Generalized Recursion Theory, 1974, North-Holland, Amsterdam.
16. Friedman, H., Iterated inductive definitions and ∑12-AC. Kino, A., Myhill, J., Vesley, R.E., (eds.) Intuirionism and Proof Theory, 1970, North-Holland, Amsterdam, 435–442.
17. Gandy, R.O., Inductive definitions. Fenstad, J.E., Hinman, P.G., (eds.) Generalized Recursion Theory, 1974, North-Holland, Amsterdam, 265–300.
18. Grzegorczyk, A., Mostowski, A., Ryll-Nardzewski, C., The classical and ω-complete arithmetic. J. Symbolic Logic 23 (1958), 188–206.
19. Grilliot, T.J., Model theory for dissecting recursion theory. Fenstad, J.E., Hinman, P.G., (eds.) Generalized Recursion Theory, 1974, North-Holland, Amsterdam, 421–428.
20. L.A. Harrington [1975] Monotone quantifiers and inductive definability, mimeographed notes.
21. L.A. Harrington & A.S. Kechris [1975] On monotone versus non-monotone induction, mimeographed notes.
22. Kleene, S.C., Introduction to Meramathematics, 1952, Van Nostrand, Princeton, NJ.
23. Kreider, D.L., Rogers, H., Constructive versions of ordinal number classes. Trans. Am. Math. Soc. 100 (1961), 325–369.
24. P. Martin-Löf [1971] Haupsatz for the intuitionistic theory of iterated inductive definitions, in: Proceedings of the Second Scandinauian Logic Symposium, edited by J.E. Fenstad, (North-Holland, Amsterdam) pp. 179–216.
25. Moschovakis, Y.N., Elementary Induction on Absrract Structures, 1974, North-Holland, Amsterdam.
26. On non-monotone inductive definability. Fund. Math. LXXXII (1974), 39–83.
27. [1976] On the basic notions in the theory of induction, preprint.
28. Putnam, H., Uniqueness ordinals in higher constructive number classes. Bar-Hillel, Y., et al. (eds.) Essays on the Foundations of Mafhernatics., 1961, Magnes Press, Jerusalem, 190–206 dedicated to A.A. Fraenkel.
29. On hierarchies and systems of notations. Proc. Am. Math. Soc. 15 (1964), 44–50.
30. Post, E., Formal reductions of the general combinatorial decision problem. Am. J. Math. 65 (1943), 197–215.
31. Richter, W., Extensions of the constructive ordinals. J. Symbolic Logic 30 (1965), 193–211.
32. Constructive transfinite number classes. Bull. Am. Math. Soc. 73 (1967), 261–265.
33. Constructively accessible ordinal numbers. J. Symbolic Logic. 33 (1968), 43–55.
34. Recursively Mahlo ordinals and inductive definitions. Candy, R.O., Yates, C.E.M., (eds.) Logic Colloquium ‘69, 1971, North-Holland, Amsterdam, 273–288.
35. [1976] The least ∑12 and reflecting ordinals. to appear.
36. RichtEr, W., Aczel, P., Inductive definitions and reflecting properties of admissible ordinals. Fenstad, J.E., Hinman, P.G., (eds.) Generalized Recursion Theory., 1974, North-Holland, Amsterdam, 301–384.
37. Smullyan, R.M., Theory of Formal Sysfems, 1961, Princeton University Press, Princeton. NJ.
38. Spector, C. [1961] Inductively defined sets of natural numbers. in: Infinistic Methods (Proceedings of the Warsaw symposium) (Pergamon Press. Oxford) pp. 97–102.
39. Zucker, J.I., Iterated inductive definitions. trees and ordinals. Troelstra, A.S., (eds.) Metamathematical Inuestigation of Intuitionistic Arithmetic and Analysis, 344, 1973, Springer, Berlin Lecture Notes in Mathematics.