On \(p\)-reducibility of computable numerations (Q5951067)

The notion of \(p\)-reducibility was introduced by the author in Mat. Sb., N. Ser. 112(154), 207-219 (1980; Zbl 0449.03037). The main result is: If \(\nu_1\) and \(\nu_2\) are two computable numberings of some family of c.e. sets, \(\nu_2<_p \nu_1\), and \(\nu_1\) is not a \(p\)-principal numbering, then there exists a computable numbering \(\nu_0\) such that \(\nu_2<_p\nu_0\) and \(\nu_0\), \(\nu_1\) are \(p\)-incomparable. As a corollary, the author proves a description of injective objects and the absence of projective objects in the category \(K_p\) of numbered sets conforming to \(p\)-reducibility.