# Categoricity over P for first order T or categoricity for phi in L_{omega_1 omega} can stop at aleph_k while holding for aleph_0, ..., aleph_{k-1}

@inproceedings{Hart1990CategoricityOP, title={Categoricity over P for first order T or categoricity for phi in L_\{omega_1 omega\} can stop at aleph_k while holding for aleph_0, ..., aleph_\{k-1\}}, author={Bradd Hart and Saharon Shelah}, year={1990} }

Suppose L is a relational language and P in L is a unary predicate. If M is an L-structure then P(M) is the L-structure formed as the substructure of M with domain {a: M models P(a)}. Now suppose T is a complete first order theory in L with infinite models. Following Hodges, we say that T is relatively lambda-categorical if whenever M, N models T, P(M)=P(N), |P(M)|= lambda then there is an isomorphism i:M-> N which is the identity on P(M). T is relatively categorical if it is relatively lambda… CONTINUE READING