Degrees of categoricity for prime and homogeneous models

We study effective categoricity for homogeneous and prime models of a complete theory. For a computable structure S, the degree of categoricity of S is the least Turing degree which can compute isomorphisms among arbitrary computable copies of S. We build new examples of degrees of categoricity for homogeneous models and for prime Heyting algebras, i.e. prime models of a complete extension of the theory of Heyting algebras. We show that 0^(ω+1) is the degree of categoricity for a homogeneous model. We prove that any Turing degree which is d.c.e. in and above 0⁽ⁿ⁾, where 3 ≤ n < ω, is the degree of categoricity for a prime Heyting algebra.