Combinations related to classes of finite and countably categorical structures and their theories

S. V. Sudoplatov

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 135-150.

Résumé

We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to closures with respect to $E$-operators and $P$-operators.

Détail

Keywords: finite structure, countably categorical structure, elementary theory, $E$-operator, $P$-operator, $e$-spectrum.

Bibliographie

[1] B. S. Baizhanov, S. V. Sudoplatov, V. V. Verbovskiy, “Conditions for non-symmetric relations of semi-isolation”, Siberian Electronic Mathematical Reports, 9 (2012), 161–184 | MR | Zbl

[2] A. Pillay, “Countable models of stable theories”, Proc. Amer. Math. Soc., 89 (1983), 666–672 | DOI | MR | Zbl

[3] E. Rosen, “Some Aspects of Model Theory and Finite Structures”, The Bulletin of Symbolic Logic, 8 (2002), 380–403 | DOI | MR | Zbl

[4] S. V. Sudoplatov, “Type reduction and powerful types”, Siberian Math. J., 33 (1992), 125–133 | DOI | MR | Zbl

[5] S. V. Sudoplatov, “Transitive arrangements of algebraic systems”, Siberian Math. J., 40 (1999), 1347–1351 | MR | Zbl

[6] S. V. Sudoplatov, “Inessential combinations and colorings of models”, Siberian Math. J., 44 (2003), 883–890 | DOI | MR | Zbl

[7] S. V. Sudoplatov, “Syntactic approach to constructions of generic models”, Algebra and Logic, 46 (2007), 134–146 | DOI | MR | Zbl

[8] S. V. Sudoplatov, “Algebras of distributions of formulas with respect to generalized semi-isolation”, Algebra and Model Theory 9, Collection of papers, NSTU, Novosibirsk, 2013, 67–100 | Zbl

[9] S. V. Sudoplatov, Group polygonometries, NSTU, Novosibirsk, 2013

[10] S. V. Sudoplatov, “Models of cubic theories”, Bulletin of the Section of Logic, 43 (2014), 19–34 | MR | Zbl

[11] S. V. Sudoplatov, “Forcing of infinity and algebras of distributions of binary semi-isolating formulas for strongly minimal theories”, Mathematics and Statistics, 2 (2014), 183–187

[12] S. V. Sudoplatov, Classification of countable models of complete theories, NSTU, Novosibirsk, 2014 | MR

[13] S. V. Sudoplatov, P. Tanović, “Semi-isolation and the strict order property”, Notre Dame J. of Formal Logic, 56 (2015), 555–572 | DOI | MR | Zbl

[14] S. V. Sudoplatov, Combinations of structures, 2016, 19 pp., arXiv: 1601.00041v1 [math.LO]

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

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

[17] S. V. Sudoplatov, Relative $e$-spectra and relative closures for families of theories, 2017, 15 pp., arXiv: 1701.00206v1 [math.LO]

[18] S. V. Sudoplatov, On semilattices and lattices for families of theories, 2017, 8 pp., arXiv: 1701.00208v1 [math.LO]

[19] J. Väänänen, “Pseudo-finite model theory”, Matematica Contemporanea, 24 (2003), 169–183 | MR | Zbl

[20] B. Zil'ber, Structural approximation, Preprint, Oxford University, Oxford, 2010, 27 pp.