A note on r-maximal subspaces of \(V_{\infty}\) (Q800918)

\textit{G. Metakides} and \textit{A. Nerode} [Ann. Math. Logic 11, 147-171 (1977; Zbl 0389.03019)] introduced the study of the fully effective vector space \(V_{\infty}\) and the lattice \(L(V_{\infty})\) of r.e. subspaces of \(V_{\infty}\). \textit{I. Kalantari} [J. Symb. Logic 43, 293- 303 (1978; Zbl 0403.03034)] introduced the notion of major subspace and proved their existence developing a method of building subspaces of \(V_{\infty}\). \textit{I. Kalantari} and \textit{A. Retzlaff} [J. Symb. Logic 42, 481-491 (1977; Zbl 0383.03033)] refined this method and produced ''super-maximal'' subspaces of \(V_{\infty}\). We further extend Kalantari's basic method of construction to construct subspaces of \(V_{\infty}\) with new properties, focusing on the notions major and r- maximal.