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Page 1185 of Mathematical Reviews Vol. 44, Issue 6
[page]
1972
Mathematical Reviews
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He does this by constructing a minimal degree d, for each ae 2" in a way that makes these minimal degrees very independent of one another.
J. R. Shoenfield (Durham, N.C.)
6493
Herman, G. ...
A countable set of notations O* and hierarchy of level 2 jumps J,5(a € O%) is defined and the usual properties, such as uniqueness, are established. ...
Page 944 of Mathematical Reviews Vol. 37, Issue 5
[page]
1969
Mathematical Reviews
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Hensel, Gustav; Putnam, Hilary 5096 On the notational independence of various hierarchies of degrees of unsolvability.
J. Symbolic Logic 30 (1965), 69-86. ...
Marek (Warsaw)
Hirose, Ken 5095 An investigation on degrees of unsolvability.
J. Math. Soc. ...
Book Review: Computability and unsolvability
1959
Bulletin of the American Mathematical Society
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Part III continues the development started in Part I. It is concerned with the Kleene hierarchy, computable functional, the recursion theorems, and degrees of unsolvability. ...
The unsolvability of the word problem for groups (shown by Novikoff and, independently, Boone) is stated, but not proved. ...
doi:10.1090/s0002-9904-1959-10329-3
fatcat:ycmrl3br5rgqli3j5lnvoj6cie
Quantitative and qualitative information in computations
1980
Information and Control
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One is the minimal-program complexity of the sequences and represents a quantitative information content, and the other is the degree of unsolvability of the underlying set and represents a qualitative ...
The major conclusion from this work is that with few exceptions these measures of information content are unrelated. Various tradeotis between these measures are also demonstrated. ...
define the complexity classes, By deg A we will denote the degree of unsolvability of the set A, and A' will denote the jump of the set A. ...
doi:10.1016/s0019-9958(80)90615-4
fatcat:f62popptmjfcpprgkjlh6njg4u
JSL volume 30 issue 4 Cover and Back matter
1965
Journal of Symbolic Logic (JSL)
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CRESSWELL 65 On the notational independence of various hierarchies of degrees of unsolvability. ...
Trial and error predicates and the solution to a problem of Mostowski. An algebraic study of Diodorean modal systems. By R. A. BULL . . 58 On the logic of incomplete answers. By M. J. ...
doi:10.1017/s0022481200055845
fatcat:bxhbwrkfrrfsdfmdd7lrvqzth4
Degrees of Transducibility
[chapter]
2015
Lecture Notes in Computer Science
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This preorder induces equivalence classes, called degrees, and a partial order on the degrees. For Turing Machines, this structure of degrees is well-studied and known as degrees of unsolvability. ...
In contrast with the degrees of unsolvability, very little is known about the structure of degrees obtained from finite state transducers or Mealy Machines. ...
The ensuing hierarchy of degrees of unsolvability has been widely studied in the 60's and 70's of the last century and later. We use the notion of degrees of unsolvability as a guiding analogy. ...
doi:10.1007/978-3-319-23660-5_1
fatcat:57hl6axxanbi7gqagwhifm5dru
Secure and Scalable Key Aggregation Scheme for Cloud Storage
2015
Journal of the Korea Industrial Information Systems Research
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And recently, many companies support cloud storages to meet the requirements of the customers. ...
Especially in the business field where various companies collaborate, data sharing is an essential functionality to enhance their work performance. ...
However many unsolved security problems in CS restrict the extension of cloud technology to various IT areas. The basic security problem is originated by the remote place to store user's data. ...
doi:10.9723/jksiis.2015.20.2.011
fatcat:7osiaxzvtjeypet23u5e3qpwmy
Hyperarithmetical Sets
[chapter]
2016
Outstanding Contributions to Logic
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The first, key question was how to measure the unsolvability of a set of natural numbers. 1A. Post's degrees of unsolvability. ...
In modern notation, the Borel hierarchy {Σ 0 : < Ω 1 } (on N ) is defined by setting
3C. ...
To see that it is the least model of (∆ 1 1 -Comp), assume that F satisfies (∆ 1 1 -Comp) and prove by induction on that ∆ ⊆ F using Theorem 3I.1. (2) Suppose that (∀s)(∃α ∈ HYP)(∃ ∈ HYP)ϕ(s, , α) with ...
doi:10.1007/978-3-319-41842-1_5
fatcat:qbbfx2gan5ddjcjx6vrnswr2v4
Page 6027 of Mathematical Reviews Vol. , Issue 2000i
[page]
2000
Mathematical Reviews
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Summary: “We show that the length of the naturally occurring jump hierarchy of the infinite time Turing degrees is precisely a, and construct continuum many incomparable such degrees which are minimal ...
and closed under composition and “bounded recursion on notation”. ...
On a subrecursive hierarchy and primitive recursive degrees
1959
Transactions of the American Mathematical Society
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Pursuit of this interest led therefore to the devising of various hierarchies of recursive functions. ...
In [4, §6] the notion of primitive recursive degree is introduced in analogy to that of degree of recursive unsolvability (general recursive degree) of Kleene and Post [5] . ...
doi:10.1090/s0002-9947-1959-0126377-3
fatcat:7tshveruejbfjostbqhhed2fp4
On a Subrecursive Hierarchy and Primitive Recursive Degrees
1959
Transactions of the American Mathematical Society
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Pursuit of this interest led therefore to the devising of various hierarchies of recursive functions. ...
In [4, §6] the notion of primitive recursive degree is introduced in analogy to that of degree of recursive unsolvability (general recursive degree) of Kleene and Post [5] . ...
doi:10.2307/1993169
fatcat:gxkidhbui5cxhd2f2rzc4htdo4
Degrees of computability
1956
Transactions of the American Mathematical Society
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In the theory of recursive functions, several decision problems have been proved unsolvable. ...
A decision problem arises when we are confronted with a set TV of mathematical objects and a subset S of 7Y. We desire a mechanical procedure which will operate on elements of TV, deter- ...
In all cases, the notation chosen to represent elements of N will be a natural one. ...
doi:10.1090/s0002-9947-1956-0085187-3
fatcat:a64bfycbcrdylczg2vklfvs37a
Mass problems associated with effectively closed sets
2011
Tohoku mathematical journal
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One of these results answers a question which arises naturally from the Kolmogorov interpretation. ...
The purpose of this paper is to summarize recent investigations into the lattice of Muchnik degrees of nonempty effectively closed sets in Euclidean space. Let Ew be this lattice. ...
consistent axiomatizable extension of one of these. 6 Indeed, the recursive homeomorphism type of C(T ) is independent of the choice of T . ...
doi:10.2748/tmj/1325886278
fatcat:nsfrryez4rdrxjikkwclfokely
Emil Post
[chapter]
2009
Handbook of the History of Logic
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The biographical essay [Gleiser, 1980] is a very informative source on Post's life. The description of Post's papers was obtained from the web site of the American Philosophical Society, which is ...
ACKNOWLEDGEMENTS My greatest debt is to Martin Davis, whose editorial work and writings on Post were indispensable in preparing this chapter. ...
This definition results in a hierarchy of degrees of unsolvability, with respect to Turing reducibility. ...
doi:10.1016/s1874-5857(09)70016-0
fatcat:erwzbkejovc7vfrx2xbqqmtybe
Standardization and Böhm Trees for Λμ-Calculus
[chapter]
2010
Lecture Notes in Computer Science
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the failure of separation in Parigot's original λµ-calculus. ...
Then, we study innite Λµ-Böhm trees, which are Böhm-like trees for Λµ-calculus; this allows to strengthen the separation results that we established previously for Λµ-calculus and to shed a new light on ...
Acknowledgments: The author wishes to thank Simona Ronchi della Rocca as well as Kazushige Terui for helpful discussions on the material of this paper. ...
doi:10.1007/978-3-642-12251-4_11
fatcat:niemqq2cf5aczbwgdvortwjoqa
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