This article is cited in 10 papers

Mathematical logic, algebra and number theory

Definable families of theories, related calculi and ranks

N. D. Markhabatov^a, S. V. Sudoplatov<sup>bca

a</sup> Novosibirsk State Technical University, 20, K. Marx ave., Novosibirsk, 630073, Russia
^b Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russia
^c Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Abstract: We consider sentence-definable and diagram-definable subfamilies of given families of theories, calculi for these subfamilies, as well dynamics and characteristics of these subfamilies with respect to rank and degree.

Keywords: family of theories, definable subfamily, calculus, rank, degree.

UDC: 510.67

MSC: 03C30, 03C15, 03C50, 03F03, 54A05

Received April 20, 2020, published May 22, 2020

Language: English

DOI: 10.33048/semi.2020.17.048

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