Hyperanalytic predicates

Author:
Yiannis N. Moschovakis

Journal:
Trans. Amer. Math. Soc. **129** (1967), 249-282

MSC:
Primary 02.72

DOI:
https://doi.org/10.1090/S0002-9947-1967-0236010-2

MathSciNet review:
0236010

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References | Similar Articles | Additional Information

**[1]**D. A. Clarke,*Hierarchies of predicates of finite types*, Mem. Amer. Math. Soc. No.**51**(1964), 95. MR**0175759****[2]**R. O. Gandy,*General recursive functionals of finite type and hierarchies of functions*, mimeographed copy of paper presented at the Sympos. Math. Logic, Univ. of Clermont Ferrand, June 1962. (Similar material was presented by Gandy at the Summer School in Math. Logic, Univ. of Leicester, August 1965, and a paper will appear in the Proceedings of that Summer School.)**[3]**Stephen Cole Kleene,*Introduction to metamathematics*, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR**0051790****[4]**S. C. Kleene,*On the forms of the predicates in the theory of constructive ordinals. II*, Amer. J. Math.**77**(1955), 405–428. MR**0070595**, https://doi.org/10.2307/2372632**[5]**S. C. Kleene,*Quantification of number-theoretic functions*, Compositio Math.**14**(1959), 23–40. MR**0103822****[6]**S. C. Kleene,*Recursive functionals and quantifiers of finite types. I*, Trans. Amer. Math. Soc.**91**(1959), 1–52. MR**0102480**, https://doi.org/10.1090/S0002-9947-1959-0102480-9**[7]**S. C. Kleene,*Recursive functionals and quantifiers of finite types. II*, Trans. Amer. Math. Soc.**108**(1963), 106–142. MR**0153557**, https://doi.org/10.1090/S0002-9947-1963-0153557-4**[8]**H. Rogers, Jr.,*Recursive functions and effective computability*, McGraw-Hill, New York.**[9]**J. R. Shoenfield,*A hierarchy for objects of type 2*, Abstract 65T-173, Notices Amer. Math. Soc.**81**(1965), 369.**[10]**Clifford Spector,*Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics*, Proc. Sympos. Pure Math., Vol. V, American Mathematical Society, Providence, R.I., 1962, pp. 1–27. MR**0154801**

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DOI:
https://doi.org/10.1090/S0002-9947-1967-0236010-2

Article copyright:
© Copyright 1967
American Mathematical Society