Geodesic
Minimality conditions, topologies, and ranks for spherically ordered theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 600-615

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

The class of ordered structures is productively studied both in order to classify them and in various applications connected with comparing of objects and information structuring. Important particular kinds of ordered structures are represented by $o$-minimal, weakly $o$-minimal and circularly minimal ones as well as their variations including definable minimality. We show that the well developed powerful theory for $o$-minimality, circular minimality, and definable minimality is naturally spread for the spherical case. Reductions of spherical orders to linear ones, called the linearizations, and back reconstructions, called the spherifications, are examined. Neighbourhoods for spherically ordered structures and their topologies are studied. It is proved that related topological spaces can be $T_0$-spaces, $T_1$-spaces and Hausdorff ones. These cases are characterized by the cardinality estimates of the universe. Definably minimal linear orders, their definably minimal extensions and restrictions as well as spherical ones are described. The notion of convexity rank is generalized for spherically ordered theories, and values for the convexity rank are realized in weakly spherically minimal theories which are countably categorical.
Keywords: spherical order, weak spherical minimality, definable minimality, topology, convexity rank. 
@article{SEMR_2023_20_2_a2,
     author = {S. V. Sudoplatov},
     title = {Minimality conditions, topologies, and ranks for spherically ordered theories},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {600--615},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a2/}
}
TY  - JOUR
AU  - S. V. Sudoplatov
TI  - Minimality conditions, topologies, and ranks for spherically ordered theories
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2023
SP  - 600
EP  - 615
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a2/
LA  - en
ID  - SEMR_2023_20_2_a2
ER  - 
%0 Journal Article
%A S. V. Sudoplatov
%T Minimality conditions, topologies, and ranks for spherically ordered theories
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2023
%P 600-615
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a2/
%G en
%F SEMR_2023_20_2_a2
S. V. Sudoplatov. Minimality conditions, topologies, and ranks for spherically ordered theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 600-615. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a2/