Undecidability of \(L(F_{\infty})\) and other lattices of r.e. substructures
This paper establishes the undecidability of \(L(F_{\infty})\). The result is established in a general setting along the lines of that of \textit{J. B. Remmel} [Ann. Math. Logic 18, 153-191 (1980; Zbl 0471.03037)]. It applies to the lattices of r.e. substructures of - for example - (all) Steinitz systems, free groups, Boolean algebras, and a wide class of modules over locally computable rings. The proof builds a special type of r-maximal set, and, using this, codes Boolean pairs into the relevant lattice. Related applications are discussed.
scientific article; zbMATH DE number 3974953
scientific article