6 found
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  1.  9
    Recursion Theory and Algebra.G. Metakides, A. Nerode, J. N. Crossley, Iraj Kalantari & Allen Retzlaff - 1986 - Journal of Symbolic Logic 51 (1):229-232.
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  2.  14
    Maximal Vector Spaces Under Automorphisms of the Lattice of Recursively Enumerable Vector Spaces.Iraj Kalantari & Allen Retzlaff - 1977 - Journal of Symbolic Logic 42 (4):481-491.
  3.  11
    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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  4.  11
    Simple and Hyperhypersimple Vector Spaces.Allen Retzlaff - 1978 - Journal of Symbolic Logic 43 (2):260-269.
    Let $V_\propto$ be a fixed, fully effective, infinite dimensional vector space. Let $\mathscr{L}(V_\propto)$ be the lattice consisting of the recursively enumerable (r.e.) subspaces of $V_\propto$ , under the operations of intersection and weak sum (see § 1 for precise definitions). In this article we examine the algebraic properties of $\mathscr{L}(V_\propto)$ . Early research on recursively enumerable algebraic structures was done by Rabin [14], Frolich and Shepherdson [5], Dekker [3], Hamilton [7], and Guhl [6]. Our results are based upon the more (...)
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  5.  17
    Direct Summands of Recursively Enumerable Vector Spaces.Allen Retzlaff - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (19-24):363-372.
  6.  8
    Direct Summands of Recursively Enumerable Vector Spaces.Allen Retzlaff - 1979 - Mathematical Logic Quarterly 25 (19‐24):363-372.