Degree structures: Local and global investigations

Degree structures: Local and global investigations

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by Richard A. Shore

Venue:	Bulletin of Symbolic Logic
Citations:	4 - 1 self

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@ARTICLE{Shore_degreestructures:,
    author = {Richard A. Shore},
    title = {Degree structures: Local and global investigations},
    journal = {Bulletin of Symbolic Logic},
    year = {},
    volume = {12},
    pages = {2006}
}

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Abstract

$1. Introduction. The occasion of a retiring presidential address seems like a time to look back, take stock and perhaps look ahead.

Citations

411	Recursively Enumerable Sets and Degrees - Soare - 1987
66	Degrees of Unsolvability - Lerman - 1983
58	Degrees of unsolvability - Sacks - 1963
44	Two recursively enumerable sets of incomparable degrees of unsolvability - Friedberg - 1957
40	On the degrees less than 0 - Sacks
36	Lower bounds for pairs of recursively enumerable degrees - Lachlan - 1966
32	An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees - Ambos-Spies, Jockusch, et al. - 1984
31	The recursively enumerable degrees are dense - Sacks - 1964
30	On the unsolvability of the problem of reducibility in the theory of algorithms - Muchnik - 1956
26	Array nonrecursive sets and multiple permitting arguments - Downey, Jockusch, et al. - 1990
26	On the degrees of recursive unsolvability - Spector - 1956
25	Embedding nondistributive lattices in the recursively enumerable degrees - Lachlan - 1970
23	Recursive enumerability and the jump operator - Sacks - 1963
21	Minimal degrees and the jump operator - Cooper - 1973
21	1968], Distributive initial segments of the degrees of unsolvability - Lachlan
16	Decidability in degree structures - Slaman, Woodin
15	First order theory of the degrees of recursive unsolvability - Simpson
14	Decidability and invariant classes for degree structures - Lerman, Shore - 1988
12	Lattice embeddings into the recursively enumerable degrees - Ambos-Spies, Lerman - 1986
12	Some problems of definability in recursive function theory - Rogers - 1965
12	Initial segments of the degrees of unsolvability - Lerman - 1971
12	Finitely generated codings and the degrees r.e. in a degree d - Shore - 1982
11	On a conjecture of Kleene and - Cooper - 1993
10	1982], The undecidability of the recursively enumerable degrees (research announcement - Harrington, Shelah
10	1984], The Elementary Theory of the Recursively Enumerable Degrees is not ℵ0-categorical - Lerman, Shore, et al.
9	1954] The upper semi-lattice of degrees of recursive unsolvability - Kleene, Post
9	A finite lattice without critical triple that cannot be embedded into the enumerable Turing degrees - Lempp, Lerman - 1997
9	First-order theory of the degrees of recursive unsolvability - Simpson - 1977
9	1979], The homogeneity conjecture - Shore - 1979
8	The decidability of the existential theory of the poset of the recursively enumerable degrees with jump relations - Lempp, Lerman - 1996
8	Array nonrecursive sets and multiple permitting arguments - Stob - 1990
8	1981], The theory of the degrees below 0 0 - Shore - 1981
7	1983], Independence results on the global structure of the Turing degrees - Groszek, Slaman
7	2001], Extension of embeddings in the computably enumerable degrees - Slaman, Soare
7	Jump embeddings in the Turing degrees - Hinman, Slaman - 1991
7	Minimal covers and arithmetical sets - Jockusch, Soare - 1970
7	A minimal degree less than 00 - Sacks - 1961
7	1999], The recursively enumerable degrees - Shore
6	The Turing universe is not rigid - Cooper - 1997
6	Shore [1984], Pseudo jump operators II: Transfinite iterations, hierarchies, and minimal covers - A
6	Local initial segments of the Turing degrees - Kjos-Hanssen
6	Shore [1980a], Reducibility orderings: theories, definability and automorphisms - Nerode, A
6	On the 89-sentences of ff-recursion theory, in Generalized Recursion Theory - Shore
6	Beyond Godel's theorem: the failure to capture information content - Cooper - 1997
5	1971], Initial segments of the degrees of unsolvability, Ann - Lerman
5	Embedding Jump Upper Semilattices into the Turing Degrees - Montalbán
4	1989], The recursively enumerable degrees have infinitely many one-types, Ann. Pure and Applied Logic 44 - Ambos-Spies, Soare - 1987
4	Epstein [1979], Degrees of Unsolvability: Structure and Theory - L
4	Double jump inversion and strong minimal covers - GABAY - 2004
4	Embedding finite lattices into the computably enumerable degrees - a status survey - Lempp, Lerman, et al. - 2002