Equivalence of some definitions of recursion in a higher type object1
Equivalence of some definitions of recursion in a higher type object1
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DOI：
10.2307/2272241
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发表时间：
--
期刊：
影响因子：
0.57
通讯作者：
F. Lowenthal
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文献类型：
--
作者：
F. Lowenthal
In [4] Kleene gave a definition of recursive functionals of finite type. Later Sacks [5] and Harrington [2] gave definitions of recursion in normal functionals of finite type. These definitions, that Sacks and Harrington assumed equivalent as far as normal objects are concerned, are nevertheless very different: Kleene's definition is given in terms of an inductive definition; Sacks uses simultaneously a hierarchy (the S σ F's) and induction on the ordinals and on the type; Harrington's universe does not use the induction on the type but uses a hierarchy as Shoenfield [6]. In this paper we prove in detail that, as was expected, the three definitions are equivalent.
