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Article

Keywords:
model theory; universal homogeneous model; model companion; amalgamation class
Summary:
We give a self-contained introduction to universal homogeneous models (also known as rich models) in a general context where the notion of morphism is taken as primitive. We produce an example of an amalgamation class where each connected component has a saturated rich model but the theory of the rich models is not model-complete.
References:
[BaShe] Baldwin J., Shelah S.: Model companions of $T_ Aut$ for stable $T$. Notre Dame J. Formal Logic 42 (2001), no. 3, 129–142. DOI 10.1305/ndjfl/1063372196 | MR 2010177 | Zbl 1034.03040
[BaZa] Barbina S., Zambella D.: Generic expansions of countable models. preprint, http://arxiv.org/abs/1011.0120
[BHMW] Baudisch A., Hils M., Pizarro A.M., Wagner F.O.: Die böse Farbe. J. Inst. Math. Jussieu 8 (2009), no. 3, 415–443. DOI 10.1017/S1474748008000091 | MR 2516302 | Zbl 1179.03041
[ChaPi] Chatzidakis Z., Pillay A.: Generic structures and simple theories. Ann. Pure Appl. Logic 95 (1998), no. 1–3, 71–92. DOI 10.1016/S0168-0072(98)00021-9 | MR 1650667 | Zbl 0929.03043
[Goode] Goode J.B.: Hrushovski's geometries. in Proceedings of the 7th Easter Conference on Model Theory (Wendisch-Rietz, 1989), Humboldt-Univ., Berlin, 1989, pp. 106–117. MR 1045014 | Zbl 0689.03016
[Hru] Hrushovski E.: A new strongly minimal set. Ann. Pure Appl. Logic 62 (1993), no. 2, 147–166. DOI 10.1016/0168-0072(93)90171-9 | MR 1226304 | Zbl 0804.03020
[KueLa] Kueker D.W., Laskowski M.C.: On generic structures. Notre Dame J. Formal Logic 33 (1992), no. 2, 175–183. DOI 10.1305/ndjfl/1093636094 | MR 1167973 | Zbl 0768.03010
[Lasc] Lascar D.: Les beaux automorphismes. Arch. Math. Logic 31 (1991), no. 1, 55–68. DOI 10.1007/BF01370694 | MR 1126353 | Zbl 0766.03022
[Poiz] Poizat B.: Le carré de l'égalité. J. Symbolic Logic 64 (1999), no. 3, 1339–1355. DOI 10.2307/2586634 | MR 1779766 | Zbl 0938.03058
[Zam] Zambella D.: Krull dimension of types in a class of first-order theories. Turkish J. Math.(to appear). MR 2839726
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