Geodesic
Algorithmic Compexity of Countable Models of Strongly Minimal Theories
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 2, pp. 38-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A positive solution of S. Lempp’s hypothesis is obtained. We’ve proved, that all countable models of strongly minimal models are computable with oracle $0^2$, if this theory has at least one computable model. 
@article{VNGU_2008_8_2_a3,
     author = {S. S. Goncharov},
     title = {Algorithmic {Compexity} of {Countable} {Models} of {Strongly} {Minimal} {Theories}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {38--53},
     year = {2008},
     volume = {8},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a3/}
}
TY  - JOUR
AU  - S. S. Goncharov
TI  - Algorithmic Compexity of Countable Models of Strongly Minimal Theories
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2008
SP  - 38
EP  - 53
VL  - 8
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a3/
LA  - ru
ID  - VNGU_2008_8_2_a3
ER  - 
%0 Journal Article
%A S. S. Goncharov
%T Algorithmic Compexity of Countable Models of Strongly Minimal Theories
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2008
%P 38-53
%V 8
%N 2
%U http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a3/
%G ru
%F VNGU_2008_8_2_a3
S. S. Goncharov. Algorithmic Compexity of Countable Models of Strongly Minimal Theories. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 2, pp. 38-53. http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a3/

[1] Ash C. J., Knight J. F., Computable Structures and the Hyperarithmetical Hierarchy, Elsevier Science, 2000 | Zbl

[2] Baldwin J. T., Lachlan A. H., “On strongly minimal sets”, J. Symbolic Logic, 36 (1971), 79–96 | DOI | MR | Zbl

[3] Buechler S. A., Essential Stability Theory, Springer-Verlag, Heidelberg, 1996 | MR | Zbl

[4] Keisler G., Chen Ch. Ch., Teoriya modelei, Mir, M., 1977 | MR

[5] Ershov Yu. L., “Konstruktivnye modeli”, Izbrannye voprosy algebry i logiki, 1974, 111–130 | Zbl

[6] Ershov Yu. L., Goncharov S. S., Constructive Models, Siberian School of Algebra and Logic, Consultants Bureau, N.Y., 2000 | MR | Zbl

[7] Ershov Yu., Goncharov S., “Elementary Theories and Their Constructive Models. Handbook of Recursive Mathematics”, v. 1, Stud. Logic Found. Math., 138, Amsterdam, 1998, 261–287 | DOI | MR

[8] Fokina E., “O slozhnosti kategorichnykh teorii s vychislimymi modelyami”, Vestn. Novosib. gos. un-ta. Seriya: Matematika, mekhanika i informatika, 5:2 (2005), 78–86

[9] Goncharov S. S., “Konstruktivnye modeli $\omega_1$-kategorichnykh teorii”, Matematicheskie zametki, 23 (1978), 885–888 | MR | Zbl

[10] Goncharov S. S., “Computability and Models”, Mathematical Problems from Applied Logic II, International Mathematical, 5, Springer, 2007, 99–216 | MR | Zbl

[11] Goncharov S., Harizanov V., Lempp S. et al., “Trivial, Strongly Minimal Theories are Model Complete after Naming Constants”, Proc. Amer. Math. Soc., 131 (2003), 3901–3912 | DOI | MR | Zbl

[12] Goncharov S., Khusainov B., “Slozhnost kategorichnykh teorii s vychislimymi modelyami”, DAN, 385:3 (2002), 299–301 | MR | Zbl

[13] Goncharov S., Khusainov B., “O slozhnosti teorii vychislimykh $\aleph_1$-kategorichnykh modelei”, Vestn. Novosib. gos. un-ta. Seriya: Matematika, mekhanika i informatika, 1:2 (2001), 63–76 | MR

[14] Goncharov S., Khusainov B., “Slozhnost teorii vychislimykh kategorichnykh modelei”, Algebra i logika, 43:6 (2004), 650–665 | MR | Zbl

[15] Goncharov S., Khoussainov B., “Open Problems in the Theory of Constructive Algebraic Systems”, Contemporary Mathematics, 257, AMS, 2000, 145–170 | DOI | MR | Zbl

[16] Harrington L., “Recursively Presented Prime Models”, J. Symbolic Logic, 39 (1974), 305–309 | DOI | MR | Zbl

[17] Herwig B., Lempp St., Ziegler M., “Constructive Models of Uncountably Categorical Theories”, Proc. Amer. Math. Soc., 127 (1999), 3711–3719 | DOI | MR | Zbl

[18] Hodges W., A Shorter Model Theory, Cambridge Univ. Press, Cambridge, 1997 | MR

[19] Khisamiev N., “Silno konstruktivnye modeli razreshimykh teorii”, Izv. AN Kaz. SSR. Seriya. Fiz.-Mat., 1 (1974), 83–84 | MR

[20] Kudaibergenov K., “O konstruktivnykh modelyakh nerazreshimykh teorii”, Sib. mat. zhurn., 21:5 (1980), 155–158 | MR | Zbl

[21] Khoussainov B., Nies A., Shore R., “On Recursive Models of Theories”, Notre Dame J. Formal Logic, 38:2 (1997), 165–178 | DOI | MR | Zbl

[22] Morley M., “Categoricity in Power”, Trans. Amer. Math. Soc., 114 (1965), 514–538 | DOI | MR | Zbl

[23] Morley M., “Countable Models of $\aleph_1$-categorical Theories”, Israel J. Math., 5 (1967), 65–72 | DOI | MR | Zbl

[24] Nies A. O., “A New Spectrum of Recursive Models”, Notre Dame J. Formal Logic, 40 (1999), 307–314 | DOI | MR | Zbl

[25] Khoussainov B., Lempp S., Laskowski M. et al., “On the Computability-Theoretical Complexity of Trivial Strongly Minimal Models”, Proc. of Amer. Math. Soc., 135:11 (2007), 3711–3721 | DOI | MR | Zbl

[26] Pillay A., Geometric Stability Theory, Clarendon Press, Oxford, 1996 | MR | Zbl

[27] Rodzhers Kh., Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972 | MR

[28] Soare R. I., Recursively Enumerable Sets and Degrees, Springer-Verlag, Berlin, 1987, 243 pp. | MR