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Recursion Theory and Algebra

G. Metakides, A. Nerode, J. N. Crossley, Iraj Kalantari & Allen Retzlaff

Journal of Symbolic Logic 51 (1):229-232 (1986)

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The undecidability of the lattice of R.E. closed subsets of an effective topological space.Sheryl Silibovsky Brady & Jeffrey B. Remmel - 1987 - Annals of Pure and Applied Logic 35 (C):193-203.details The first-order theory of the lattice of recursively enumerable closed subsets of an effective topological space is proved undecidable using the undecidability of the first-order theory of the lattice of recursively enumerable sets. In particular, the first-order theory of the lattice of recursively enumerable closed subsets of Euclidean n -space, for all n , is undecidable. A more direct proof of the undecidability of the lattice of recursively enumerable closed subsets of Euclidean n -space, n ⩾ 2, is provided using (...) Download Export citation Bookmark
Complexity-theoretic algebra II: Boolean algebras.A. Nerode & J. B. Remmel - 1989 - Annals of Pure and Applied Logic 44 (1-2):71-99.details Download Export citation Bookmark 5 citations
A note on r-maximal subspaces of V[infinity].David R. Guichard - 1984 - Annals of Pure and Applied Logic 26 (1):1.details Download Export citation Bookmark
Undecidability of L(F∞) and other lattices of r.e. substructures.R. G. Downey - 1986 - Annals of Pure and Applied Logic 32:17-26.details Download Export citation Bookmark 8 citations
Degrees of convex dependence in recursively enumerable vector spaces.Thomas A. Nevins - 1993 - Annals of Pure and Applied Logic 60 (1):31-47.details Let W be a recursively enumerable vector space over a recursive ordered field. We show the Turing equivalence of the following sets: the set of all tuples of vectors in W which are linearly dependent; the set of all tuples of vectors in W whose convex closures contain the zero vector; and the set of all pairs of tuples in W such that the convex closure of X intersects the convex closure of Y. We also form the analogous sets consisting (...) Download Export citation Bookmark
Maximal theories.R. G. Downey - 1987 - Annals of Pure and Applied Logic 33 (C):245-282.details Download Export citation Bookmark 8 citations
(1 other version)Automorphisms and Recursive Structures.R. G. Downey & J. B. Remmel - 1987 - Mathematical Logic Quarterly 33 (4):339-345.details Download Export citation Bookmark
Recursively enumerable vector spaces.G. Metakides - 1977 - Annals of Mathematical Logic 11 (2):147.details Download Export citation Bookmark 60 citations
Recursive properties of relations on models.Geoffrey R. Hird - 1993 - Annals of Pure and Applied Logic 63 (3):241-269.details Hird, G.R., Recursive properties of relations on models, Annals of Pure and Applied Logic 63 241–269. We prove general existence theorems for recursive models on which various relations have specified recursive properties. These capture common features of results in the literature for particular algebraic structures. For a useful class of models with new relations R, S, where S is r.e., we characterize those for which there is a recursive model isomorphic to on which the relation corresponding to S remains r.e., (...) Download Export citation Bookmark 6 citations
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.details 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 (...) Download Export citation Bookmark
Foundations of recursive model theory.Terrence S. Millar - 1978 - Annals of Mathematical Logic 13 (1):45.details Download Export citation Bookmark 19 citations
Recursion theory on algebraic structures with independent sets.J. B. Remmel - 1980 - Annals of Mathematical Logic 18 (2):153.details Download Export citation Bookmark 11 citations
Recursively enumerable Boolean algebras.J. B. Remmel - 1978 - Annals of Mathematical Logic 15 (1):75.details Download Export citation Bookmark 18 citations
Recursion theory and ordered groups.R. G. Downey & Stuart A. Kurtz - 1986 - Annals of Pure and Applied Logic 32:137-151.details Download Export citation Bookmark 10 citations
Computable isomorphisms, degree spectra of relations, and Scott families.Bakhadyr Khoussainov & Richard A. Shore - 1998 - Annals of Pure and Applied Logic 93 (1-3):153-193.details The spectrum of a relation on a computable structure is the set of Turing degrees of the image of R under all isomorphisms between and any other computable structure . The relation is intrinsically computably enumerable if its image under all such isomorphisms is c.e. We prove that any computable partially ordered set is isomorphic to the spectrum of an intrinsically c.e. relation on a computable structure. Moreover, the isomorphism can be constructed in such a way that the image of (...) Download Export citation Bookmark 16 citations
Automorphisms of substructure lattices in recursive algebra.David R. Guichard - 1983 - Annals of Pure and Applied Logic 25 (1):47-58.details Download Export citation Bookmark 9 citations
(1 other version)Automorphisms and Recursive Structures.R. G. Downey & J. B. Remmel - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (4):339-345.details Download Export citation Bookmark

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