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.
References
[1] Baur, W., "$\aleph \sb0$"-categorical modules", The Journal of Symbolic Logic, vol. 40 (1975), pp. 213--20. MR0369047 0309.02059 10.2307/2271901 euclid.jsl/1183739382
[1] Baur, W., "$\aleph \sb0$"-categorical modules", The Journal of Symbolic Logic, vol. 40 (1975), pp. 213--20. MR0369047 0309.02059 10.2307/2271901 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. MR533805 0401.03012 10.1016/0021-8693(79)90230-8[2] Baur, W., G. Cherlin, and A. Macintyre, "Totally categorical groups and rings", Journal of Algebra, vol. 57 (1979), pp. 407--440. MR533805 0401.03012 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. MR1066691 0813.20002[3] Cameron, P. J., Oligomorphic Permutation Groups, vol. 152 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1990. MR1066691 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. MR1650667 0929.03043 10.1016/S0168-0072(98)00021-9[4] Chatzidakis, Z., and A. Pillay, "Generic structures and simple theories", Annals of Pure and Applied Logic, vol. 95 (1998), pp. 71--92. MR1650667 0929.03043 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. MR1325469 0812.03016[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. MR1325469 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. MR1231710 0788.03039 10.1112/jlms/s2-48.2.204[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. MR1231710 0788.03039 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. MR1777786 0930.03034 10.2307/2586500 euclid.jsl/1183745809
[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. MR1777786 0930.03034 10.2307/2586500 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. MR1014866 0649.03018 10.1112/plms/s3-59.3.439[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. MR1014866 0649.03018 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. MR975912 0667.03027 10.1093/qmath/39.4.483[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. MR975912 0667.03027 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. MR1162490 0723.20001 10.1112/plms/s3-65.1.121[10] Truss, J. K., "Generic automorphisms of homogeneous structures", Proceedings of the London Mathematical Society. Third Series, vol. 65 (1992), pp. 121--41. MR1162490 0723.20001 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. MR739577 0593.16019 10.1016/0168-0072(84)90014-9[11] Ziegler, M., "Model theory of modules", Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149--213. MR739577 0593.16019 10.1016/0168-0072(84)90014-9