Geodesic
Algebras for definable families of theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 600-608.

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We consider algebras associated with sentence-definable and diagram-definable subfamilies of families of theories. Topological properties and ranks for these algebras are characterized.
Keywords: family of theories, definable subfamily, algebra for definable subfamilies, rank, degree. 
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N. D. Markhabatov; S. V. Sudoplatov. Algebras for definable families of theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 600-608. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a8/

[1] N. D. Markhabatov, S. V. Sudoplatov, Definable families of theories, related calculi and ranks, Novosibirsk, 2019, arXiv: 1901.11011v1 [math.LO] | MR | Zbl

[2] S. V. Sudoplatov, “Combinations of structures”, The Bulletin of Irkutsk State University. Series “Mathematics”, 24 (2018), 65–84 | DOI | MR

[3] S. V. Sudoplatov, “Closures and generating sets related to combinations of structures”, Reports of Irkutsk State University. Series “Mathematics”, 16 (2016), 131–144 | MR | Zbl

[4] S. V. Sudoplatov, “Families of language uniform theories and their generating sets”, Reports of Irkutsk State University. Series “Mathematics”, 16 (2016), 62–76 | Zbl

[5] S. V. Sudoplatov, “Combinations related to classes of finite and countably categorical structures and their theories”, Siberian Electronic Mathematical Reports, 14 (2017), 135–150 | MR | Zbl

[6] S. V. Sudoplatov, “Relative $e$-spectra and relative closures for families of theories”, Siberian Electronic Mathematical Reports, 14 (2017), 296–307 | MR | Zbl

[7] S. V. Sudoplatov, “On semilattices and lattices for families of theories”, Siberian Electronic Mathematical Reports, 14 (2017), 980–985 | MR | Zbl

[8] S. V. Sudoplatov, Approximations of theories, 2019, arXiv: 1901.08961v1 [math.LO]

[9] S. V. Sudoplatov, Ranks for families of theories and their spectra, 2019, arXiv: 1901.08464v1 [math.LO]

[10] N. D. Markhabatov, S. V. Sudoplatov, Ranks for families of all theories of given languages, 2019, arXiv: 1901.09903v1 [math.LO] | MR | Zbl

[11] S. Feferman, R. Vaught, “The first order properties of products of algebraic systems”, Fund. Math., 47 (1959), 57–103 | DOI | MR | Zbl

[12] M. Morley, “Categoricity in Power”, Transactions of the American Mathematical Society, 114:2 (1965), 514–538 | DOI | MR | Zbl

[13] S. Koppelberg, Handbook of Boolean Algebras, v. 1, eds. J. D. Monk, R. Bonnet, North-Holland, Amsterdam, 1989 | MR | Zbl

[14] W. J. Blok, D. Pigozzi, Algebraizable logics, Memoirs of the AMS, 77, no. 396, 1989 | DOI | MR

[15] P. Hinman, Fundamentals of Mathematical Logic, AK Peters, Wellesley, Massachusets, 2005 | MR | Zbl