Notre Dame Journal of Formal Logic

Ages of Expansions of ω-Categorical Structures

A. Ivanov and K. Majcher

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Abstract

The age of a structure M is the set of all isomorphism types of finite substructures of M. We study ages of generic expansions of ω-stable ω-categorical structures.

Article information

Source
Notre Dame J. Formal Logic, Volume 48, Number 3 (2007), 371-380.

Dates
First available in Project Euclid: 13 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1187031409

Digital Object Identifier
doi:10.1305/ndjfl/1187031409

Mathematical Reviews number (MathSciNet)
MR2336353

Zentralblatt MATH identifier
1146.03014

Subjects
Primary: 03C45: Classification theory, stability and related concepts [See also 03C48]

Keywords
omega-stable omega-categorical structures age generic expansions

Citation

Ivanov, A.; Majcher, K. Ages of Expansions of ω-Categorical Structures. Notre Dame J. Formal Logic 48 (2007), no. 3, 371--380. doi:10.1305/ndjfl/1187031409. https://projecteuclid.org/euclid.ndjfl/1187031409


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References

  • [1] Baur, W., "$\aleph \sb0$"-categorical modules", The Journal of Symbolic Logic, vol. 40 (1975), pp. 213--20.
    Mathematical Reviews (MathSciNet): MR0369047
    Zentralblatt MATH: 0309.02059
    Digital Object Identifier: doi:10.2307/2271901
    Project Euclid: euclid.jsl/1183739382
  • [2] Baur, W., G. Cherlin, and A. Macintyre, "Totally categorical groups and rings", Journal of Algebra, vol. 57 (1979), pp. 407--440.
    Mathematical Reviews (MathSciNet): MR533805
    Zentralblatt MATH: 0401.03012
    Digital Object Identifier: doi:10.1016/0021-8693(79)90230-8
  • [3] Cameron, P. J., Oligomorphic Permutation Groups, vol. 152 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1990.
    Mathematical Reviews (MathSciNet): MR1066691
    Zentralblatt MATH: 0813.20002
  • [4] Chatzidakis, Z., and A. Pillay, "Generic structures and simple theories", Annals of Pure and Applied Logic, vol. 95 (1998), pp. 71--92.
    Mathematical Reviews (MathSciNet): MR1650667
    Zentralblatt MATH: 0929.03043
    Digital Object Identifier: doi:10.1016/S0168-0072(98)00021-9
  • [5] Evans, D. M., "Examples of $\aleph\sb 0$"-categorical structures, pp. 33--72 in Automorphisms of First-Order Structures, edited by R. Kaye and H. D. Macpherson, Oxford Science Publications, Oxford University Press, New York, 1994.
    Mathematical Reviews (MathSciNet): MR1325469
    Zentralblatt MATH: 0812.03016
  • [6] Hodges, W., I. Hodkinson, D. Lascar, and S. Shelah, "The small index property for $\omega$"-stable $\omega$-categorical structures and for the random graph, Journal of the London Mathematical Society. Second Series, vol. 48 (1993), pp. 204--218.
    Mathematical Reviews (MathSciNet): MR1231710
    Zentralblatt MATH: 0788.03039
    Digital Object Identifier: doi:10.1112/jlms/s2-48.2.204
  • [7] Ivanov, A. A., "Generic expansions of $\omega$"-categorical structures and semantics of generalized quantifiers, The Journal of Symbolic Logic, vol. 64 (1999), pp. 775--89.
    Mathematical Reviews (MathSciNet): MR1777786
    Zentralblatt MATH: 0930.03034
    Digital Object Identifier: doi:10.2307/2586500
    Project Euclid: euclid.jsl/1183745809
  • [8] Kantor, W. M., M. W. Liebeck, and H. D. Macpherson, "$\aleph\sb 0$"-categorical structures smoothly approximated by finite substructures", Proceedings of the London Mathematical Society. Third Series, vol. 59 (1989), pp. 439--63.
    Mathematical Reviews (MathSciNet): MR1014866
    Zentralblatt MATH: 0649.03018
    Digital Object Identifier: doi:10.1112/plms/s3-59.3.439
  • [9] Macpherson, H. D., "Absolutely ubiquitous structures and $\aleph\sb 0$"-categorical groups, The Quarterly Journal of Mathematics. Oxford. Second Series, vol. 39 (1988), pp. 483--500.
    Mathematical Reviews (MathSciNet): MR975912
    Zentralblatt MATH: 0667.03027
    Digital Object Identifier: doi:10.1093/qmath/39.4.483
  • [10] Truss, J. K., "Generic automorphisms of homogeneous structures", Proceedings of the London Mathematical Society. Third Series, vol. 65 (1992), pp. 121--41.
    Mathematical Reviews (MathSciNet): MR1162490
    Zentralblatt MATH: 0723.20001
    Digital Object Identifier: doi:10.1112/plms/s3-65.1.121
  • [11] Ziegler, M., "Model theory of modules", Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149--213.
    Mathematical Reviews (MathSciNet): MR739577
    Zentralblatt MATH: 0593.16019
    Digital Object Identifier: doi:10.1016/0168-0072(84)90014-9

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