Geodesic
Properties of existentially closed companions
Algebra i logika, Tome 57 (2018) no. 3, pp. 321-337.

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

Necessary and sufficient conditions are stated for an arbitrary theory to be an elementary theory for a class of its existentially closed models. Conditions are given under which some existentially closed model simultaneously realizes one maximal existential type and omits another. We also prove a theorem on a prime existentially closed model over a maximal existential type. Considerable complexity of existentially closed structures and their theories was noted by A. Macintyre. Therefore, the examples of existentially closed companions having any finite or countable number of pairwise non elementarily equivalent existentially closed models constructed here are of interest.
Keywords: elementary theory, existentially closed model, existentially closed companion, existential type. 
@article{AL_2018_57_3_a4,
     author = {A. T. Nurtazin},
     title = {Properties of existentially closed companions},
     journal = {Algebra i logika},
     pages = {321--337},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_3_a4/}
}
TY  - JOUR
AU  - A. T. Nurtazin
TI  - Properties of existentially closed companions
JO  - Algebra i logika
PY  - 2018
SP  - 321
EP  - 337
VL  - 57
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2018_57_3_a4/
LA  - ru
ID  - AL_2018_57_3_a4
ER  - 
%0 Journal Article
%A A. T. Nurtazin
%T Properties of existentially closed companions
%J Algebra i logika
%D 2018
%P 321-337
%V 57
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2018_57_3_a4/
%G ru
%F AL_2018_57_3_a4
A. T. Nurtazin. Properties of existentially closed companions. Algebra i logika, Tome 57 (2018) no. 3, pp. 321-337. http://geodesic.mathdoc.fr/item/AL_2018_57_3_a4/

[1] A. Robinson, On the metamathematics of algebra, Stud. Logic Found. Math., North-Holland Publ. Co., Amsterdam, 1951 | MR | Zbl

[2] Dzh. Barvais, Spravochnaya kniga po matematicheskoi logike. Ch. 1: Teoriya modelei, v 4-kh chastyakh, ed. Dzh. Barvais, Nauka, M., 1982

[3] A. T. Nurtazin, “Schetnye ekzistentsialno zamknutye modeli universalno aksiomatiziruemykh teorii”, Matem. trudy, 18:1 (2015), 48–97 | DOI | MR | Zbl

[4] R. Fraïsse, “Sur quelques classifications des systèmes de rélations”, Publ. Sci. Univ. Alger. Sér. A, 1 (1955), 35–182 | Zbl

[5] Z. G. Khisamiev, “Ob ekzistentsialno zamknutykh kompanonakh koltsa tselykh chisel”, Mezhd. konf. “Maltsevskie chteniya”, posvyasch. 75-letiyu Yu. L. Ershova (3–7 maya 2015 g., Novosibirsk), Tez. dokl., IM SO RAN i NGU, Novosibirsk, 2015, 202 http://math.nsc.ru/conference/malmeet/15/malmeet15.pdf