Geodesic
Relatively Hyperimmune Relations on Structures
Algebra i logika, Tome 43 (2004) no. 2, pp. 170-183.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathcal{A}$ be a computable structure and let $R$ be an additional relation on its domain. We establish a necessary and sufficient condition for the existence of an isomorphic copy $\mathcal{B}$ of $\mathcal{A}$ such that the image of $R$ ($\lnot R$) is $h$-simple ($h$-immune) relative to $\mathcal{B}$.
Keywords: computable structure, relatively hyperimmune relation, relatively hypersimple relation. 
@article{AL_2004_43_2_a2,
     author = {S. S. Goncharov and Ch. F. McCoy and J. F. Knight and V. S. Harizanova},
     title = {Relatively {Hyperimmune} {Relations} on {Structures}},
     journal = {Algebra i logika},
     pages = {170--183},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2004_43_2_a2/}
}
TY  - JOUR
AU  - S. S. Goncharov
AU  - Ch. F. McCoy
AU  - J. F. Knight
AU  - V. S. Harizanova
TI  - Relatively Hyperimmune Relations on Structures
JO  - Algebra i logika
PY  - 2004
SP  - 170
EP  - 183
VL  - 43
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2004_43_2_a2/
LA  - ru
ID  - AL_2004_43_2_a2
ER  - 
%0 Journal Article
%A S. S. Goncharov
%A Ch. F. McCoy
%A J. F. Knight
%A V. S. Harizanova
%T Relatively Hyperimmune Relations on Structures
%J Algebra i logika
%D 2004
%P 170-183
%V 43
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2004_43_2_a2/
%G ru
%F AL_2004_43_2_a2
S. S. Goncharov; Ch. F. McCoy; J. F. Knight; V. S. Harizanova. Relatively Hyperimmune Relations on Structures. Algebra i logika, Tome 43 (2004) no. 2, pp. 170-183. http://geodesic.mathdoc.fr/item/AL_2004_43_2_a2/

[1] R. I. Soare, Recursively enumerable sets and degrees. A study of computable functions and computably generated sets, Springer-Verlag, Berlin, 1987 | MR

[2] J. C. E. Dekker, “A theorem on hypersimple sets”, Proc. Am. Math. Soc., 5:5 (1954), 791–796 | DOI | MR | Zbl

[3] C. G. Jockusch, Jr., “Semirecursive sets and positive reducibility”, Trans. Am. Math. Soc., 131:2 (1968), 420–436 | DOI | MR | Zbl

[4] G. Hird, “Recursive properties of intervals of recursive linear orders”, Logical Methods, eds. J. N. Crossley, J. B. Remmel, R. A. Shore, M. E. Sweedler, Birkhauser, Boston, 1993, 422–437 | MR | Zbl

[5] J. B. Remmel, “Recursive isomorphism types of recursive Boolean algebras”, J. Symb. Log., 46:3 (1981), 572–594 | DOI | MR | Zbl

[6] S. S. Goncharov, V. S. Harizanov, J. F. Knight, C. McCoy, “Simple and immune relations on countable structures”, Arch. Math. Logic, 42:3 (2003), 279–291 | DOI | MR | Zbl

[7] G. R. Hird, “Recursive properties of relations on models”, Ann. Pure Appl. Logic, 63:3 (1993), 241–269 | DOI | MR | Zbl

[8] V. S. Harizanov, “Turing degrees of hypersimple relations on computable structures”, Ann. Pure Appl. Logic, 121:2 (2003), 209–226 | DOI | MR | Zbl

[9] C. J. Ash, J. F. Knight, Computable structures and the hyperarithmetical hierarchy, Elsevier, Amsterdam, 2000 | MR

[10] C. Ash, J. Knight, M. Manasse, T. Slaman, “Generic copies of countable structures”, Ann. Pure Appl. Logic, 42:3 (1989), 195–205 | DOI | MR | Zbl

[11] J. Chisholm, “Effective model theory vs. recursive model theory”, J. Symb. Log., 55:3 (1990), 1168–1191 | DOI | MR | Zbl

[12] A. Nerode, J. B. Remmel, “A survey of lattices of r.e. substructures”, Recursion Theory, Proc. Symp. Pure Math., 42, eds. A. Nerode, R. Shore, Am. Math. Soc., Providence, RI, 1985, 323–375 | MR | Zbl

[13] J. F. Knight, “Degrees coded in jumps of orderings”, J. Symb. Log., 51:4 (1986), 1034–1042 | DOI | MR | Zbl