Soare, Bounding homogeneous models

Soare, Bounding homogeneous models

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by Barbara F. Csima , Valentina S. Harizanov , Denis R. Hirschfeldt , Robert I. Soare

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@MISC{Csima_soare,bounding,
    author = {Barbara F. Csima and Valentina S. Harizanov and Denis R. Hirschfeldt and Robert I. Soare},
    title = {Soare, Bounding homogeneous models},
    year = {}
}

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Abstract

A Turing degree d is homogeneous bounding if every complete decidable (CD) theory has a d-decidable homogeneous model A, i.e., the elementary diagram D e (A) has degree d. It follows from results of Macintyre and Marker that every PA degree (i.e., every degree of a complete extension of Peano Arithmetic) is homogeneous bounding. We prove that in fact a degree is homogeneous bounding if and only if it is a PA degree. We do this by showing that there is a single CD theory T such that every homogeneous model of T has a PA degree. 1

Citations

396	Model Theory - Chang - 1973
136	Subsystems of Second Order Arithmetic - Simpson - 1999
103	Π 0 1 classes and degrees of theories - Soare - 1972
62	Soare, Recursively Enumerable Sets and Degrees - I - 1987
50	Model Theory : An Introduction - Marker - 2002
32	Algebras of sets binumerable in complete extensions of arithmetic - Scott - 1962
30	Degrees coded into jumps of orderings - Knight - 1986
26	Recursively Presentable Prime Models - Harrington - 1974
20	Degrees of unsolvability: a survey of results - Simpson - 1977
19	Foundations of recursive model theory - Millar - 1978
18	Degrees in which recursive sets are uniformly recursive. Canadian Journal of Mathematics, 24:1092– 1099 - Jockusch - 1972
13	Soare, Computability Theory and Applications - I
12	Strongly Constructive Models of a Decidable Theory - Khisamiev - 1974
11	Soare, Bounding prime models - Csima, Hirschfeldt, et al.
11	Denumerable models of complete theories / R - Vaught - 1961
10	Pure computable model theory, Handbook of Recursive Mathematics - Harizanov - 1999
9	1959], Non-Archimedian models of arithmetic - Tennenbaum
8	Computability-theoretic complexity of countable structures - Harizanov
8	Degrees of recursively saturated models - Macintyre, Marker - 1984
8	Decidable Models - Morley
7	Degree spectra of prime models - Csima
6	Degrees of models - Shoenfield - 1960
5	Computable trees, prime models, and relative decidability - Hirschfeldt
5	Degrees of models of true arithmetic - Marker
4	Strong constructivizability of homogeneous models - Goncharov - 1978
4	Nurtazin, Constructive models of complete solvable theories, Algebra and Logic 12 - Goncharov, T - 1973
4	Soare, Degrees of members of - I - 1972
3	A totally transcendental decidable theory without constructivizable homogeneous models, Algebra and Logic - Goncharov - 1980
3	Homogeneous models and decidability - Millar - 1980
3	Soare, Degrees of members of \Pi 01 classes - Jockusch, I - 1972
2	Bounding saturated models - Harris
2	The degree spectra of homogeneous models - Lange
2	A characterization of the 0-basis homogeneous bounding degrees - Lange
2	Pure recursive model theory, Handbook of Computability Theory - Millar - 1999
2	On the number of homogeneous models of a given power - Morley, Keisler - 1967
2	Criterion for strong constructivizability of a homogeneous model, Algebra and Logic 17 - Peretyat’kin - 1978
1	Soare, The computable content of Vaughtian models - Lange, I
1	Soare, Computability of homogeneous models - Lange, I
1	Bounding saturated models, to appear. [13 - Harris
1	Soare, \Pi 01 classes and degrees of theories - I - 1972
1	The degree spectra of homogeneous models, to appear. [20] K. Lange, A characterization of the 0-basis homogeneous bounding degrees - Lange