Finitely generated submodels of an uncountably categorical homogeneous structure

Mathematical Logic Quarterly 50 (1):77 (2004)
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Abstract

We generalize the result of non-finite axiomatizability of totally categorical first-order theories from elementary model theory to homogeneous model theory. In particular, we lift the theory of envelopes to homogeneous model theory and develope theory of imaginaries in the case of ω-stable homogeneous classes of finite U-rank

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10.1002/malq.200310079

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Citations of this work

Quasiminimal structures, groups and Zariski-like geometries.Tapani Hyttinen & Kaisa Kangas - 2016 - Annals of Pure and Applied Logic 167 (6):457-505.
Simplicity and uncountable categoricity in excellent classes.Tapani Hyttinen & Olivier Lessmann - 2006 - Annals of Pure and Applied Logic 139 (1):110-137.
Locally modular geometries in homogeneous structures.Tapani Hyttinen - 2005 - Mathematical Logic Quarterly 51 (3):291.

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References found in this work

ℵ0-Categorical, ℵ0-stable structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
Strong splitting in stable homogeneous models.Tapani Hyttinen & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):201-228.
Ranks and pregeometries in finite diagrams.Olivier Lessmann - 2000 - Annals of Pure and Applied Logic 106 (1-3):49-83.
ℵ0-Categorical, ℵ0-stable structures.Gregory Cherlin, Leo Harrington & Alistair H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.

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