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  1. C. J. Ash (2000). Computable Structures and the Hyperarithmetical Hierarchy. Elsevier.
    This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...)
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  2. C. J. Ash (1986). Stability of Recursive Structures in Arithmetical Degrees. Annals of Pure and Applied Logic 32 (2):113-135.
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  3.  1
    C. J. Ash & J. F. Knight (1990). Pairs of Recursive Structures. Annals of Pure and Applied Logic 46 (3):211-234.
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  4.  2
    C. J. Ash (1990). Labelling Systems and R.E. Structures. Annals of Pure and Applied Logic 47 (2):99-119.
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  5. C. J. Ash (1987). Categoricity in Hyperarithmetical Degrees. Annals of Pure and Applied Logic 34 (1):1-14.
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  6.  7
    C. J. Ash & J. F. Knight (1994). Mixed Systems. Journal of Symbolic Logic 59 (4):1383-1399.
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  7. C. J. Ash & J. F. Knight (1994). Ramified Systems. Annals of Pure and Applied Logic 70 (3):205-221.
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  8.  10
    C. J. Ash & R. G. Downey (1984). Decidable Subspaces and Recursively Enumerable Subspaces. Journal of Symbolic Logic 49 (4):1137-1145.
    A subspace V of an infinite dimensional fully effective vector space V ∞ is called decidable if V is r.e. and there exists an r.e. W such that $V \oplus W = V_\infty$ . These subspaces of V ∞ are natural analogues of recursive subsets of ω. The set of r.e. subspaces forms a lattice L(V ∞ ) and the set of decidable subspaces forms a lower semilattice S(V ∞ ). We analyse S(V ∞ ) and its relationship with L(V (...)
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  9.  4
    C. J. Ash (1991). A Construction for Recursive Linear Orderings. Journal of Symbolic Logic 56 (2):673-683.
    We re-express a previous general result in a way which seems easier to remember, using the terminology of infinite games. We show how this can be applied to construct recursive linear orderings, showing, for example, that if there is a ▵ 0 2β + 1 linear ordering of type τ, then there is a recursive ordering of type ω β · τ.
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  10.  1
    C. J. Ash & J. F. Knight (1995). Possible Degrees in Recursive Copies. Annals of Pure and Applied Logic 75 (3):215-221.
    Let be a recursive structure, and let R be a recursive relation on . Harizanov isolated a syntactical condition which is necessary and sufficient for to have recursive copies in which the image of R is r.e. of arbitrary r.e. degree. We had conjectured that a certain extension of Harizanov's syntactical condition would be necessary and sufficient for to have recursive copies in which the image of R is ∑α0 of arbitrary ∑α0 degree, but this is not the case. Here (...)
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  11. C. J. Ash & John W. Rosenthal (1986). Intersections of Algebraically Closed Fields. Annals of Pure and Applied Logic 30 (2):103-119.
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  12.  2
    C. J. Ash & J. F. Knight (1997). Possible Degrees in Recursive Copies II. Annals of Pure and Applied Logic 87 (2):151-165.
    We extend results of Harizanov and Barker. For a relation R on a recursive structure /oA, we give conditions guaranteeing that the image of R in a recursive copy of /oA can be made to have arbitrary ∑α0 degree over Δα0. We give stronger conditions under which the image of R can be made ∑α0 degree as well. The degrees over Δα0 can be replaced by certain more general classes. We also generalize the Friedberg-Muchnik Theorem, giving conditions on a pair (...)
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  13. C. J. Ash, P. Cholak & J. F. Knight (1997). Permitting, Forcing, and Copying of a Given Recursive Relation. Annals of Pure and Applied Logic 86 (3):219-236.
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  14. C. J. Ash, J. F. Knight & J. B. Remmel (1997). Quasi-Simple Relations in Copies of a Given Recursive Structure. Annals of Pure and Applied Logic 86 (3):203-218.
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  15.  1
    C. J. Ash (1975). Sentences with Finite Models. Mathematical Logic Quarterly 21 (1):401-404.
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  16. C. J. Ash (1984). Review: Leo Harrington, Recursively Presentable Prime Models; Terrence S. Millar, Foundations of Recursive Model Theory; Terrence S. Millar, A Complete, Decidable Theory with Two Decidable Models. [REVIEW] Journal of Symbolic Logic 49 (2):671-672.
     
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  17.  9
    C. J. Ash (1994). On Countable Fractions From an Elementary Class. Journal of Symbolic Logic 59 (4):1410-1413.
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  18. C. J. Ash (1992). Generalizations of Enumeration Reducibility Using Recursive Infinitary Propositional Sentences. Annals of Pure and Applied Logic 58 (3):173-184.
    Ash, C.J., Generalizations of enumeration reducibility using recursive infinitary propositional sentences, Annals of Pure and Applied Logic 58 173–184. We consider the relation between sets A and B that for every set S if A is Σ0α in S then B is Σ0β in S. We show that this is equivalent to the condition that B is definable from A in a particular way involving recursive infinitary propositional sentences. When α = β = 1, this condition is that B is (...)
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  19. C. J. Ash, J. F. Knight, B. Balcar, T. Jech, J. Zapletal & D. Rubric (1997). Hella, L., Kolaitis, PG and Luosto, K., How to Define a Linear. Annals of Pure and Applied Logic 87:269.
     
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  20. C. J. Ash (1995). Knight, JF, See Ash, CJ (3). Annals of Pure and Applied Logic 75:313.
     
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  21. C. J. Ash & J. F. Knight (1990). Pairs of Computable Structures. Annals of Pure and Applied Logic 46:211-234.
     
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