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Page 1185 of Mathematical Reviews Vol. 44, Issue 6
[page]

1972
*
Mathematical Reviews
*

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. ...##
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Page 944 of Mathematical Reviews Vol. 37, Issue 5
[page]

1969
*
Mathematical Reviews
*

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. ...##
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Book Review: Computability and unsolvability

1959
*
Bulletin of the American Mathematical Society
*

Part III continues

doi:10.1090/s0002-9904-1959-10329-3
fatcat:ycmrl3br5rgqli3j5lnvoj6cie
*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. ...##
###
Quantitative and qualitative information in computations

1980
*
Information and Control
*

*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. ...

##
###
JSL volume 30 issue 4 Cover and Back matter

1965
*
Journal of Symbolic Logic (JSL)
*

CRESSWELL 65

doi:10.1017/s0022481200055845
fatcat:bxhbwrkfrrfsdfmdd7lrvqzth4
*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. ...##
###
Degrees of Transducibility
[chapter]

2015
*
Lecture Notes in Computer Science
*

This preorder induces equivalence classes, called

doi:10.1007/978-3-319-23660-5_1
fatcat:57hl6axxanbi7gqagwhifm5dru
*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. ...##
###
Secure and Scalable Key Aggregation Scheme for Cloud Storage

2015
*
Journal of the Korea Industrial Information Systems Research
*

And recently, many companies support cloud storages to meet

doi:10.9723/jksiis.2015.20.2.011
fatcat:7osiaxzvtjeypet23u5e3qpwmy
*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. ...##
###
Hyperarithmetical Sets
[chapter]

2016
*
Outstanding Contributions to Logic
*

*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 ...

##
###
Page 6027 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
*
Mathematical Reviews
*

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
*

Pursuit

doi:10.1090/s0002-9947-1959-0126377-3
fatcat:7tshveruejbfjostbqhhed2fp4
*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] . ...##
###
On a Subrecursive Hierarchy and Primitive Recursive Degrees

1959
*
Transactions of the American Mathematical Society
*

Pursuit

doi:10.2307/1993169
fatcat:gxkidhbui5cxhd2f2rzc4htdo4
*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] . ...##
###
Degrees of computability

1956
*
Transactions of the American Mathematical Society
*

In

doi:10.1090/s0002-9947-1956-0085187-3
fatcat:a64bfycbcrdylczg2vklfvs37a
*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*. ...##
###
Mass problems associated with effectively closed sets

2011
*
Tohoku mathematical journal
*

*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 . ...

##
###
Emil Post
[chapter]

2009
*
Handbook of the History of Logic
*

*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. ...

##
###
Standardization and Böhm Trees for Λμ-Calculus
[chapter]

2010
*
Lecture Notes in Computer Science
*

*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. ...

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