Ranks for families of theories and their spectra Full article
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Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962 |
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| Output data | Year: 2021, Volume: 42, Number: 12, Pages: 2959-2968 Pages count : 10 DOI: 10.1134/S1995080221120313 | ||||
| Tags | : family of theories, rank, degree, E-closure, e-spectrum | ||||
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Abstract:
We define ranks and degrees for families of theories, similar to Morley rank and degree, as well as Cantor–Bendixson rank and degree, and the notion of totally transcendental family of theories. Bounds for e-spectra with respect to ranks and degrees are found. It is shown that the ranks and the degrees are preserved under E-closures and values for the ranks and the degrees are characterized. Criteria for totally transcendental families in terms of cardinality of E-closure and of the e-spectrum value, for a countable language, are proved.
Cite:
Sudoplatov S.V.
Ranks for families of theories and their spectra
Lobachevskii Journal of Mathematics. 2021. V.42. N12. P.2959-2968. DOI: 10.1134/S1995080221120313 WOS Scopus РИНЦ OpenAlex
Ranks for families of theories and their spectra
Lobachevskii Journal of Mathematics. 2021. V.42. N12. P.2959-2968. DOI: 10.1134/S1995080221120313 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Apr 7, 2021 |
| Accepted: | Apr 22, 2021 |
| Published print: | Dec 15, 2021 |
| Published online: | Dec 15, 2021 |
Identifiers:
| Web of science: | WOS:000730385600030 |
| Scopus: | 2-s2.0-85121366319 |
| Elibrary: | 47327865 |
| OpenAlex: | W4205467473 |