On Kierstead’s conjecture

Abstract

© 2019 American Mathematical Society. We settle the long-standing Kierstead conjecture in the negative. We do this by constructing a computable linear order with no rational subintervals, where every block has order type finite or ζ, and where every computable copy has a strongly nontrivial Π01 automorphism. We also construct a strongly η-like linear order where every block has size at most 4 with no rational subinterval such that every Δ02 isomorphic computable copy has a nontrivial Π01 automorphism.