Determining automorphisms of the recursively enumerable sets
Richard A. Shore · Proceedings of the American Mathematical Society · 1977
We answer two questions of A. Nerode and give information about how the structure of E ∗ {\mathcal {E}^\ast } , the lattice of r.e. sets modulo finite sets, is determined by various subclasses. Theorem. If C ∗ {\mathcal {C}^\ast } is any nontrivial recursively invariant subclass of E ∗ {\mathcal {E}^\ast } , then any automorphism of E ∗ {\mathcal {E}^\ast } is determined uniquely by its action on C ∗ {\mathcal {C}^\ast } . Theorem. If C ∗ {\mathcal {C}^\ast } is the class of recursive sets modulo finite sets or M ∗ ⊆ C ∗ ⊆ S ∗ {\mathcal {M}^\ast } \subseteq {\mathcal {C}^\ast } \subseteq {\mathcal {S}^\ast } ( M ∗