Geodesic
Existentially closed and maximal models in positive logic
Algebra i logika, Tome 51 (2012) no. 6, pp. 748-765
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that a subclass of positively existentially closed models of any finitely axiomatizable $h$-universal class in a predicate signature is axiomatizable. We construct examples suggesting the necessity of these conditions for the given subclass to be axiomatizable. The concept of an $h$-maximal model is introduced. It is shown that a subclass of $h$-maximal models of any finitely axiomatizable $h$-universal class is also finitely axiomatizable. Moreover, the set of positively existentially closed models in an $h$-universally axiomatizable class coincides with the set of positively existentially closed models in its subclass of $h$-maximal models.
Keywords: finitely axiomatizable $h$-universal class, positively existentially closed model. 
@article{AL_2012_51_6_a3,
     author = {A. Kungozhin},
     title = {Existentially closed and maximal models in positive logic},
     journal = {Algebra i logika},
     pages = {748--765},
     year = {2012},
     volume = {51},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2012_51_6_a3/}
}
TY  - JOUR
AU  - A. Kungozhin
TI  - Existentially closed and maximal models in positive logic
JO  - Algebra i logika
PY  - 2012
SP  - 748
EP  - 765
VL  - 51
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/AL_2012_51_6_a3/
LA  - ru
ID  - AL_2012_51_6_a3
ER  - 
%0 Journal Article
%A A. Kungozhin
%T Existentially closed and maximal models in positive logic
%J Algebra i logika
%D 2012
%P 748-765
%V 51
%N 6
%U http://geodesic.mathdoc.fr/item/AL_2012_51_6_a3/
%G ru
%F AL_2012_51_6_a3
A. Kungozhin. Existentially closed and maximal models in positive logic. Algebra i logika, Tome 51 (2012) no. 6, pp. 748-765. http://geodesic.mathdoc.fr/item/AL_2012_51_6_a3/

[1] B. Poizat, “Univers positifs”, J. Symb. Log., 71:3 (2006), 969–976 | DOI | MR | Zbl

[2] I. Ben Yaacov, B. Poizat, “Fondements de la logique positive”, J. Symb. Log., 72:4 (2007), 1141–1162 | DOI | MR | Zbl

[3] A. Kungozhin, “Dva svoistva pozitivno ekzistentsionalno-zamknutykh modelei”, Izvestiya NAN RK, seriya fiz.-matem., 2010, no. 5(273), 18–20

[4] A. Kungozhin, “O podklasse $h$-maksimalnykh modelei $h$-universalnogo klassa”, Izvestiya NAN RK, ser. fiz.-matem., 2010, no. 6(274), 55–57

[5] R. Lyndon, “Properties preserved in subdirect products”, Pac. J. Math., 9 (1959), 155–164 | DOI | MR | Zbl