Relative categoricity in abelian groups II

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Annals of Pure and Applied Logic 158 (3):203-231 (2009)
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Abstract

We consider structures A consisting of an abelian group with a subgroup AP distinguished by a 1-ary relation symbol P, and complete theories T of such structures. Such a theory T is -categorical if T has models A of cardinality λ with AP=κ, and given any two such models A,B with AP=BP, there is an isomorphism from A to B which is the identity on AP. We classify all complete theories of such structures A in terms of the cardinal pairs in which they are categorical. We classify algebraically the A of finite order λ with AP of order κ which are -categorical

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10.1016/j.apal.2008.03.007

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The elementary theory of abelian groups.Paul C. Eklof - 1972 - Annals of Mathematical Logic 4 (2):115.
Classification theory over a predicate. I.Anand Pillay & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (4):361-376.

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