Finite condensations of recursive linear orders
This paper answers a question raised by J. Rosenstein: that of locating, in the arithmetical hierarchy, the finite condensation of a recursive linear order type. It was proved that (1) there is a recursive linear order whose finite condensation has \(\Pi_ 2-\Pi_ 1\) order type, (2) a linear order type is \(\Pi_{2n}\) iff it is the n-fold finite condensation of a recursive type, and (3) for all \(n\geq 2\) an order type is \(\Pi_ n\) iff it is \(\Sigma_ n\) presented.
finite condensation of a recursive linear order type
scientific article; zbMATH DE number 4101165