Relative Categoricity in Abelian Groups [chapter]

Wilfrid Hodges, S. Barry Cooper, John K. Truss
Models and Computability  
We consider structures A consisting of an abelian group with a subgroup A P distinguished by a 1-ary relation symbol P , and complete theories T of such structures. Such a theory T is (κ, λ)-categorical if T has models A of cardinality λ with |A P | = κ, and given any two such models A, B with A P = B P , there is an isomorphism from A to B which is the identity on A P . We state all true theorems of the form: If T is (κ, λ)-categorical then T is (κ ′ , λ ′ )-categorical. We classify the A of
more » ... classify the A of finite order λ with A P of order κ which are (κ, λ)-categorical.
doi:10.1017/cbo9780511565670.007 fatcat:ppqunbo2bbcndaxopzgeodw76i