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  1. Undecidability of L(F∞) and Other Lattices of R.E. Substructures.R. G. Downey - 1986 - Annals of Pure and Applied Logic 32 (1):17-26.
  • Bases of Supermaximal Subspaces and Steinitz Systems. I.Rod Downey - 1984 - Journal of Symbolic Logic 49 (4):1146-1159.
  • 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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  • Degree Invariance in the Π10classes.Rebecca Weber - 2011 - Journal of Symbolic Logic 76 (4):1184-1210.
    Let ℰΠ denote the collection of all Π01 classes, ordered by inclusion. A collection of Turing degrees.
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  • Classifications of Degree Classes Associated with R.E. Subspaces.R. G. Downey & J. B. Remmel - 1989 - Annals of Pure and Applied Logic 42 (2):105-124.
    In this article we show that it is possible to completely classify the degrees of r.e. bases of r.e. vector spaces in terms of weak truth table degrees. The ideas extend to classify the degrees of complements and splittings. Several ramifications of the classification are discussed, together with an analysis of the structure of the degrees of pairs of r.e. summands of r.e. spaces.
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  • Complexity-Theoretic Algebra II: Boolean Algebras.A. Nerode & J. B. Remmel - 1989 - Annals of Pure and Applied Logic 44 (1-2):71-99.
  • First-Order Theories of Abstract Dependence Relations.John T. Baldwin - 1984 - Annals of Pure and Applied Logic 26 (3):215-243.
  • On the Lattices of NP-Subspaces of a Polynomial Time Vector Space Over a Finite Field.Anil Nerode & J. B. Remmel - 1996 - Annals of Pure and Applied Logic 81 (1-3):125-170.
    In this paper, we study the lower semilattice of NP-subspaces of both the standard polynomial time representation and the tally polynomial time representation of a countably infinite dimensional vector space V∞ over a finite field F. We show that for both the standard and tally representation of V∞, there exists polynomial time subspaces U and W such that U + V is not recursive. We also study the NP analogues of simple and maximal subspaces. We show that the existence of (...)
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  • Maximal Theories.R. G. Downey - 1987 - Annals of Pure and Applied Logic 33 (3):245-282.