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  1. More Undecidable Lattices of Steinitz Exchange Systems.L. R. Galminas & John W. Rosenthal - 2002 - Journal of Symbolic Logic 67 (2):859-878.
    We show that the first order theory of the lattice $\mathscr{L}^{ (S) of finite dimensional closed subsets of any nontrivial infinite dimensional Steinitz Exhange System S has logical complexity at least that of first order number theory and that the first order theory of the lattice L(S ∞ ) of computably enumerable closed subsets of any nontrivial infinite dimensional computable Steinitz Exchange System S ∞ has logical complexity exactly that of first order number theory. Thus, for example, the lattice of (...)
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  • Recursive Constructions in Topological Spaces.Iraj Kalantari & Allen Retzlaff - 1979 - Journal of Symbolic Logic 44 (4):609-625.
    We study topological constructions in the recursion theoretic framework of the lattice of recursively enumerable open subsets of a topological space X. Various constructions produce complemented recursively enumerable open sets with additional recursion theoretic properties, as well as noncomplemented open sets. In contrast to techniques in classical topology, we construct a disjoint recursively enumerable collection of basic open sets which cannot be extended to a recursively enumerable disjoint collection of basic open sets whose union is dense in X.
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  • Automorphisms of Substructure Lattices in Recursive Algebra.David R. Guichard - 1983 - Annals of Pure and Applied Logic 25 (1):47-58.