Embedding of the First Nonconstructive Ordinal into the Rogers Semilattices of Families of Arithmetic Sets
M. Kh. Faĭzrahmanov · Siberian Mathematical Journal · 2023
We prove that there is an embedding of a linear order isomorphic to the first nonconstructive ordinal over each but the top element of the Rogers semilattice of an arbitrary $ \Sigma^{0}_{n} $ -computable family ( $ n\geq 2 $ ).