Two recursively enumerable sets of incomparable degrees of unsolvability (solution of post's problem, 1944).
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This article is published in Proceedings of the National Academy of Sciences of the United States of America.The article was published on 1957-02-15 and is currently open access. It has received 259 citations till now. The article focuses on the topics: Recursively enumerable language.read more
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Recursively enumerable sets and degrees
TL;DR: In this paper, the relation of the structure of an R set to its degree is discussed, and the infinite injury priority method is proposed to solve the problem of scaling and splitting R sets.
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Curriculum 68: Recommendations for academic programs in computer science: a report of the ACM curriculum committee on computer science
William F. Atchison,S. D. Conte,John W. Hamblen,Thomas E. Hull,Thomas A. Keenan,William B. Kehl,Edward J. McCluskey,Silvio O. Navarro,Werner C. Rheinboldt,Earl J. Schweppe,William Viavant,David M. Young +11 more
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Ramsey's Theorem and Recursion Theory
TL;DR: It is shown that if P is such a recursive partition of [ N ] n, then H ( P ) contains a set which is Π n 0 in the arithmetical hierarchy, and it is proved that for each n ≥ 2 there is a recursive partitions P of [N ] n into two classes such that H (P ) contains no Σ n 0 set.
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Lower Bounds for Pairs of Recursively Enumerable Degrees
TL;DR: In this paper, it was shown that the upper semi-lattice of the r.i.d. degrees is not a lattice, thus verifying another conjecture of Sacks ((4) 170): there exist two r.e.d degrees a, b whose greatest lower bound is 0.