Geodesic
The Tarski--Lindenbaum algebra of the class of prime models with infinite algorithmic dimensions having omega-stable theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 277-292.

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

We study the class of all prime strongly constructivizable models of infinite algorithmic dimensions having $\omega$-stable theories in a fixed finite rich signature. It is proved that the Tarski-Lindenbaum algebra of this class considered together with a Gödel numbering of the sentences is a Boolean $\Sigma^1_1$-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of Boolean $\Sigma^1_1$-algebras. This gives a characterization to the Tarski–Lindenbaum algebra of the class of all prime strongly constructivizable models of infinite algorithmic dimensions having $\omega$-stable theories.
Keywords: Tarski–Lindenbaum algebra, strongly constructive model, computable isomorphism, semantic class of models, $\omega$-stable theory, prime model. 
@article{SEMR_2024_21_1_a9,
     author = {M. G. Peretyat'kin},
     title = {The {Tarski--Lindenbaum} algebra of the class of prime models with infinite algorithmic dimensions having omega-stable theories},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {277--292},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a9/}
}
TY  - JOUR
AU  - M. G. Peretyat'kin
TI  - The Tarski--Lindenbaum algebra of the class of prime models with infinite algorithmic dimensions having omega-stable theories
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 277
EP  - 292
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a9/
LA  - en
ID  - SEMR_2024_21_1_a9
ER  - 
%0 Journal Article
%A M. G. Peretyat'kin
%T The Tarski--Lindenbaum algebra of the class of prime models with infinite algorithmic dimensions having omega-stable theories
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 277-292
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a9/
%G en
%F SEMR_2024_21_1_a9
M. G. Peretyat'kin. The Tarski--Lindenbaum algebra of the class of prime models with infinite algorithmic dimensions having omega-stable theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 277-292. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a9/