We extend Morley's Theorem to show that if a theory is κ-p-categorical for some uncountable cardinal κ, it is uncountably categorical. We then discuss ω-p-categoricity and provide examples to show that similar extensions for the Baldwin-Lachlan and Lachlan Theorems are not possible.

We extend Shelah's first many model result to show that an unstable theory has 2 κ many non-permutation group isomorphic models of size κ, where κ is an uncountable regular cardinal.

We extend Shelah's first many model result to show that an unstable theory has 2κmany non-permutation group isomorphic models of size κ, where κ is an uncountable regular cardinal.