Abstract:
We consider recursive representations for the set of rational numbers with a distinguished dense and codense subset and for some Boolean algebras with a distinguished subalgebra. We show that the rejection of recursiveness of the distinguished submodel opens up the possibility of constructing models without nontrivial automorphisms. The proof is carried out by the priority method.
Keywords:computable model, computable automorphism, group of computable automorphisms, priority method, Boolean algebra, recursively enumerable set.