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}

Bradd Hart, Saharon Shelah

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…