Theories of Rogers Semilattices of Analytical Numberings
Nikolay A. Bazhenov, Manat Mustafa, Zh. Tleuliyeva · Lobachevskii Journal of Mathematics · 2021
The paper studies Rogers semilattices, i.e. upper semilattices induced by the reducibility between numberings. Under the assumption of Projective Determinacy, we prove that for every non-zero natural number $$n$$ , there are infinitely many pairwise elementarily non-equivalent Rogers semilattices for $$\Sigma^{1}_{n}$$ -computable families.