Parameter Definability in the Recursively Enumerable Degrees

Parameter Definability in the Recursively Enumerable Degrees

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by Andre Nies

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@MISC{Nies_parameterdefinability,
    author = {Andre Nies},
    title = {Parameter Definability in the Recursively Enumerable Degrees},
    year = {}
}

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Abstract

The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the # k relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k >= 7, the k relations bounded from below by a nonzero degree are uniformly definable. As applications, we show that...

Citations

448	Model Theory - Hodges - 1993
411	Recursively Enumerable Sets and Degrees - Soare - 1987
106	Recursively enumerable sets of positive integers and their decision problems - Post - 1944
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
27	A recursively enumerable degree which will not split over all lesser ones - Lachlan
26	Interpolation and embedding in the recursively enumerable degrees - Robinson - 1971
25	Embedding nondistributive lattices in the recursively enumerable degrees - Lachlan - 1970
23	Recursive enumerability and the jump operator - Sacks - 1963
20	Recursively Enumerable Sets and Degrees. Perspectives in Mathematical Logic, Omega Series - Soare - 1987
17	Double jumps of minimal degrees - Posner - 1978
16	Decidability in degree structures - Slaman, Woodin
16	The undecidability of the recursively enumerable degrees - Harrington, Shelah - 1982
14	1981],The theory of the degrees below 0 - Shore - 1981
14	Working below a high recursively enumerable degree - Shore, Slaman
14	An almost deep degree - Cholak, Groszek, et al. - 2001
13	Lattice nonembeddings and initial segments of the recursively enumerable degrees - Downey - 1990
11	Degree theoretical splitting properties of recursively enumerable sets - Ambos-Spies, Fejer - 1988
11	On a conjecture of Kleene and - Cooper - 1993
11	Models of Peano Arithmetic, volume 15 of Oxford Logic Guides - Kaye - 1991
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	Application of model theory to degrees of unsolvability - Shoenfield - 1965
9	1979], The homogeneity conjecture - Shore - 1979
9	Relative recursive enumerability - Soare, Stob - 1982
8	Pseudo jump operators I - Shore - 1983
8	The last question on recursively enumerable many-one degrees - Nies - 1995
7	On Homogeneity and Definability in the First Order Theory of the Turing Degrees - Shore
7	1990], Working below a low2 recursively enumerable degree, Archive for - Shore, Slaman
7	1995], Degree theoretic definitions of the low 2 recursively enumerable sets - Downey, Shore - 1995
7	Coding in the lattice of enumerable sets - Harrington, Nies - 1998
6	Beyond Godel's theorem: the failure to capture information content - Cooper - 1997
6	1966], The impossibility of finding relative complements for recursively enumerable degrees - Lachlan
6	Interpretability and definability in the recursively enumerable turing-degrees - Nies, Shore, et al. - 1998
5	Slaman [1991], Degree structures - A - 1990
5	Woodin [1986], Definability in the Turing degrees - Slaman, H
5	Incomparable prime ideals of recursively enumerable degrees - Calhoun - 1993
5	Natural definability in degree structures - Shore
4	A degree theoretic definition of the ramified analytic hierarchy - Simpson - 1976
4	Shore [1981], The theory of the degrees below 0 - A
4	Model Theory. Enzyklopedia of Mathematics - Hodges - 1993
3	1980], Not every finite lattice is embeddable in the recursively enumerable degrees, Adv - Lachlan, Soare
3	1958], Solution of Post's reduction problem and of certain other problems in the theory of algorithms, Trudy Moskov Mat - Muchnik - 1958
3	Shore [1996], Lattice embeddings below a nonlow2 recursively enumerable degree - Downey, Shore