Recursion in total functionals of finite type
Feferman, Solomon
Compositio Mathematica, Tome 35 (1977), p. 3-22 / Harvested from Numdam
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Publié le : 1977-01-01
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     author = {Feferman, Solomon},
     title = {Recursion in total functionals of finite type},
     journal = {Compositio Mathematica},
     volume = {35},
     year = {1977},
     pages = {3-22},
     mrnumber = {485282},
     zbl = {0365.02030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1977__35_1_3_0}
}

Feferman, Solomon. Recursion in total functionals of finite type. Compositio Mathematica, Tome 35 (1977) pp. 3-22. http://gdmltest.u-ga.fr/item/CM_1977__35_1_3_0/

[1] S. Feferman: Ordinals and functionals in proof theory. Proc. Int'l. Cong. of Mathematicians (Nice, 1970) 1, 229-233. | MR 437318 | Zbl 0244.02010

[2] K. Gödel: Über einer bisher noch nicht benützten Erweiterung des finiten Standpunktes. Dialectica 12 (1958) 280-287. | MR 102482 | Zbl 0090.01003

[3] T.J. Grilliot: Selection functions for recursive functionals. Notre Dame J. Formal Logic 10 (1969) 225-234. | MR 265152 | Zbl 0185.02302

[4] L.A. Harrington and D.B. Macqueen: Selection in abstract recursion theory. J. Symbolic Logic 41 (1976) 153-158. | MR 441707 | Zbl 0409.03029

[5] S.C. Kleene: Countable functionals, in Constructivity in Mathematics, N-H, Amsterdam (1959) 81-100. | MR 112837 | Zbl 0100.24901

[6] S.C. Kleene: Recursive functionals and quantifiers of finite types. Trans. Amer. Math. Soc. 91 (1959) 1-52. | MR 102480 | Zbl 0088.01301

[7] G. Kreisel: Some reasons for generalizing recursion theory, in Logic Colloquium '69, N-H, Amsterdam (1971) 139-198. | MR 321679 | Zbl 0219.02027

[8] D.B. Macqueen: Post's problem for recursion in higher types. Dissertation, M.I.T. (1972).

[9] Y.N. Moschovakis: Hyperanalytic predicates. Trans. Amer. Math. Soc. 129 (1967) 249-282. | MR 236010 | Zbl 0159.01101

[10] Y.N. Moschovakis: Abstract first order computability. Trans. Amer. Math. Soc. 138 (1969) I. 427-464, II. 465-504. | MR 244045 | Zbl 0218.02038

[11] R. Platek: Foundations of recursion theory. Dissertation, Stanford Univ. (1966).

[12] G. Sacks: The 1-section of a type n object, in Generalized Recursion Theory (eds. Fenstad, Hinman), Amsterdam (1974) 81-93. | MR 398811 | Zbl 0287.02026

[13] J. Shoenfield: A hierarchy based on a type 2 object. Trans. Amer. Math. Soc. 134 (1968) 103-108. | MR 263626 | Zbl 0191.30502

[14] W.W. Tait: Infinitely long terms of transfinite type, in Formal Systems and Recursive Functions, N-H, Amsterdam (1968) 465-475.

[15] S.S. Wainer: A hierarchy for the 1-section of any type two object, J. Symbolic Logic 39 (1974) 88-94. | MR 360244 | Zbl 0299.02048

[16] H. Schwichtenberg and S.S. Wainer: Infinite terms and recursion in higher types. Kiel Proof Theory Symposion, 1974. Lecture Notes in Mathematics V. 500 (1975) (Springer, Berlin) 341-364. | MR 419199 | Zbl 0341.02033