Geodesic
$\Sigma$-Definability in Hereditarily Finite Superstructures and Pairs of Models
Algebra i logika, Tome 43 (2004) no. 4, pp. 459-481

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

We consider the problem of being $\Sigma$-definable for an uncountable model of a $c$-simple theory in hereditarily finite superstructures over models of another $c$-simple theory. A necessary condition is specified in terms of decidable models and the concept of relative indiscernibility introduced in the paper. A criterion is stated for the uncountable model of a $c$-simple theory to be $\Sigma$-definable in superstructures over dense linear orders, and over infinite models of the empty signature. We prove the existence of a $c$-simple theory (of an infinite signature) every uncountable model of which is not $\Sigma$-definable in superstructures over dense linear orders. Also, a criterion is given for a pair of models to be recursively saturated.
Keywords: $\Sigma$-definability, $c$-simple theory, model, hereditarily finite superstructure, linear order. 
@article{AL_2004_43_4_a4,
     author = {A. I. Stukachev},
     title = {$\Sigma${-Definability} in {Hereditarily} {Finite} {Superstructures} and {Pairs} of {Models}},
     journal = {Algebra i logika},
     pages = {459--481},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2004_43_4_a4/}
}
TY  - JOUR
AU  - A. I. Stukachev
TI  - $\Sigma$-Definability in Hereditarily Finite Superstructures and Pairs of Models
JO  - Algebra i logika
PY  - 2004
SP  - 459
EP  - 481
VL  - 43
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2004_43_4_a4/
LA  - ru
ID  - AL_2004_43_4_a4
ER  - 
%0 Journal Article
%A A. I. Stukachev
%T $\Sigma$-Definability in Hereditarily Finite Superstructures and Pairs of Models
%J Algebra i logika
%D 2004
%P 459-481
%V 43
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2004_43_4_a4/
%G ru
%F AL_2004_43_4_a4
A. I. Stukachev. $\Sigma$-Definability in Hereditarily Finite Superstructures and Pairs of Models. Algebra i logika, Tome 43 (2004) no. 4, pp. 459-481. http://geodesic.mathdoc.fr/item/AL_2004_43_4_a4/