Abstract: 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 ominimal and circularly minimal ones as well as their variations including de nable minimality. We show that the well developed powerful theory for o-minimality, circular minimality, and de nable minimality is naturally spread for the spherical case. Reductions of spherical orders to linear ones, called the linearizations, and back reconstructions, called the spheri cations, are examined. Neighbourhoods for spherically ordered structures and their topologies are studied. It is proved that related topological spaces can be T0-spaces, T1-spaces and Hausdor ones. These cases are characterized by the cardinality estimates of the universe. De nably minimal linear orders, their de nably 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.

Cite: Sudoplatov S.V.
Minimality conditions, topologies and ranks for spherically ordered theories
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N2. P.600-615. DOI: 10.33048/semi.2023.20.035 WOS Scopus РИНЦ

Dates:

Submitted:	Dec 25, 2022
Accepted:	Feb 15, 2023
Published print:	Jul 21, 2023
Published online:	Jul 21, 2023

Identifiers:

Web of science:	WOS:001044387500003
Scopus:	2-s2.0-85166281780
Elibrary:	82134623

Citing:

DB	Citing
Web of science	2
Scopus	2
Elibrary	2

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