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Preprint Number 275
275. Wilfrid Hodges Proof of Gaifman's conjecture for relatively categorical abelian groups Submission date: 17 October 2010. Abstract: Haim Gaifman conjectured in 1974 that if T is a complete firstorder theory which is relatively categorical over its relativisation T^P to a predicate P, then every model B of T^P can be extended to a model A of T with A^P = B. He proved this when T is rigid over P, and it holds also for some cases of relative categoricity in uncountably categorical theories. In what may be the first example going significantly beyond these two types, we show that the conjecture is true when the relatively categorical theory T is the theory of an abelian group with P selecting a subgroup. Mathematics Subject Classification: Keywords and phrases: Full text: pdf.

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