By Howard DeLong

ISBN-10: 0486139158

ISBN-13: 9780486139159

**Publish yr note:** First released in 1971

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This textual content explores the old purposes for the formation of Aristotelian common sense, the increase of mathematical common sense, the character of the formal axiomatic process and its use, and the most result of metatheory and their import.

*From 1971 edition*

Includes 22 figures and 19 tables. Appendixes. Bibliography. Indexes.

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**Extra info for A Profile of Mathematical Logic (Dover Books on Mathematics)**

**Sample text**

Kleene, Recursive functionals and quantifiers of finite type, Trans. Am. Math. Soc. 91 (1959) 1-52; 108 (1963) 106-142. A. O. M. ) Logic Colloquium '69 (North-Holland, Amsterdam, 1971) pp. 257271. B. D. dissertation, MIT (1 972). N. Moschovakis, Hyperanalytic predicates, Trans. Am. Math. Soc. 129 (1967) 249-282. [Ri] W. O. M. Yates (eds) Logic Colloquium '69 (North-Holland, Amsterdam, 1971) pp. 273-288. E. Sacks, The 1-Section of a type n object, this volume. R. Shoenfield, A hierarchy based on a type 2 object, Trans.

6. There exists a function @ partial recursive in El such that (a) F i s acceptable c=$ AT@(T, F ) is total; RECURSION IN THE SUPERJUMP 37 (b) If F is acceptable then XT@(T, F ) is the characteristic function of J F . Proof. 4 ) suchthat(b,p,m,q)isan immediate T-predecessor o f t and all immediate T-predecessors o f t are of this form; further, if 2E was applied then q = 0 or 1 depending on whether or not one of the immediate T-predecessors o f t is of the form ( b , p , m , O ) ; (4) other cases similarly.

8. For any F (a) F i s acceptable F* is total; and (b) ifk is acceptable then 1-sc(2E, F ) C 1-sc@*). Proof. 6. For (b) we define a primitive recursive f such that RECURSION IN THE SUPERJUMP { a } (m, 2E, P ) =n -+ 39 hr { f ( a , h))) (r, P * ) is the characteristic function of T&,n . The definition o f f for most cases is routine. {b}(p,m,2E,F). For any 4, let Tq be the tree with largest element ( a , m , q )and all T&,,,D(p) as immediate subtrees. Then dF(Tq)iff 4 = n. From the induction hypothesis we can define a primitive recursive g such that for all 4, hr {g(a, m , 4 ) } ( r ,P*) is the characteristic function of Tq.

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