Automorphisms of η-like Computable Linear Orderings and Kierstead's Conjecture

We develop an approach to the longstanding conjecture of H.A. Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any -like computable linear ordering B, such that B has no interval of order type η, and such that the order type of B is determined by a ₀'-limitwise monotonic maximal block function, there exists computable L≅B such that L has no nontrivial Π⁰₁ automorphism.