44 found
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  1.  17
    A. H. Lachlan (1979). Bounding Minimal Pairs. Journal of Symbolic Logic 44 (4):626-642.
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  2.  9
    G. Cherlin, L. Harrington & A. H. Lachlan (1985). ℵ0-Categorical, ℵ0-Stable Structures. Annals of Pure and Applied Logic 28 (2):103-135.
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  3.  16
    J. T. Baldwin & A. H. Lachlan (1971). On Strongly Minimal Sets. Journal of Symbolic Logic 36 (1):79-96.
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  4. A. H. Lachlan (1987). A Note on Positive Equivalence Relations. Mathematical Logic Quarterly 33 (1):43-46.
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  5.  7
    A. H. Lachlan & R. Lebeuf (1976). Countable Initial Segments of the Degrees of Unsolvability. Journal of Symbolic Logic 41 (2):289-300.
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  6. A. H. Lachlan (1968). Distributive Initial Segments of the Degrees of Unsolvability. Mathematical Logic Quarterly 14 (30):457-472.
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  7. A. H. Lachlan (1968). Degrees of Recursively Enumerable Sets Which Have No Maximal Supersets. Journal of Symbolic Logic 33 (3):431-443.
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  8.  2
    A. H. Lachlan (1990). Some Coinductive Graphs. Archive for Mathematical Logic 29 (4):213-229.
    LetT be a universal theory of graphs such that Mod(T) is closed under disjoint unions. Letℳ T be a disjoint union ℳ i such that eachℳ i is a finite model ofT and every finite isomorphism type in Mod(T) is represented in{ℳ i ∶i<Ω3}. We investigate under what conditions onT, Th(ℳ T ) is a coinductive theory, where a theory is called coinductive if it can be axiomatizated by ∃∀-sentences. We also characterize coinductive graphs which have quantifier-free rank 1.
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  9.  7
    A. H. Lachlan (1966). On the Indexing of Classes of Recursively Enumerable Sets. Journal of Symbolic Logic 31 (1):10-22.
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  10.  7
    A. H. Lachlan (1987). Complete Theories with Only Universal and Existential Axioms. Journal of Symbolic Logic 52 (3):698-711.
    Let T be a complete first-order theory over a finite relational language which is axiomatized by universal and existential sentences. It is shown that T is almost trivial in the sense that the universe of any model of T can be written $F \overset{\cdot}{\cup} I_1 \overset{\cdot}{\cup} I_2 \overset{\cdot}{\cup} \cdots \overset{\cdot}{\cup} I_n$ , where F is finite and I 1 , I 2 ,...,I n are mutually indiscernible over F. Some results about complete theories with ∃∀-axioms over a finite relational language (...)
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  11.  1
    A. H. Lachlan (1964). Standard Classes of Recursively Enumerable Sets. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 10 (2-3):23-42.
  12.  2
    A. H. Lachlan (1966). A Note on Universal Sets. Journal of Symbolic Logic 31 (4):573-574.
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  13. Michael Morley, J. T. Baldwin & A. H. Lachlan (1975). Countable Models of ℵ 1 -Categorical Theories. Journal of Symbolic Logic 40 (4):636-637.
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  14.  1
    A. H. Lachlan (1966). The Impossibility of Finding Relative Complements for Recursively Enumerable Degrees. Journal of Symbolic Logic 31 (3):434-454.
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  15.  4
    A. H. Lachlan (1975). Uniform Enumeration Operations. Journal of Symbolic Logic 40 (3):401-409.
    Sacks [2] has asked whether there exists a uniform solution to Post's problem, i.e. an enumeration operation W such that $\mathbf{d} for every degree d. It is shown here that if such an operation W exists it cannot itself in a particular technical sense be uniform. In fact, the jump operation is characterized amongst such uniform enumeration operations by the condition: $\mathbf{d} for all d. In addition, it is proved that the only other uniform enumeration operations such that d ≤ (...)
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  16.  6
    A. H. Lachlan (1963). Recursive Real Numbers. Journal of Symbolic Logic 28 (1):1-16.
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  17. A. H. Lachlan (1987). Structures Coordinatized by Indiscernible Sets. Annals of Pure and Applied Logic 34 (3):245-273.
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  18.  2
    A. H. Lachlan (1965). On Recursive Enumeration Without Repetition. Mathematical Logic Quarterly 11 (3):209-220.
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  19.  10
    A. H. Lachlan (1992). ℵ0-Categorical Tree-Decomposable Structures. Journal of Symbolic Logic 57 (2):501 - 514.
    Our purpose in this note is to study countable ℵ0-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.
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  20. A. H. Lachlan, Patrick Suppes & Daniel Lascar (1982). On the Number of Countable Models of a Countable Superstable Theory. Journal of Symbolic Logic 47 (1):215-217.
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  21. A. H. Lachlan (1978). Spectra of Ω‐Stable Theories. Mathematical Logic Quarterly 24 (9‐11):129-139.
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  22. Marian Boykan Pour-el, Hilary Putnam, William A. Howard & A. H. Lachlan (1973). Recursively Enumerable Classes and Their Application to Recursive Sequences of Formal Theories. Journal of Symbolic Logic 38 (1):155-156.
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  23.  1
    A. H. Lachlan (1970). Review: Paul R. Young, An Effective Operator, Continuous but Not Partial Recursive. [REVIEW] Journal of Symbolic Logic 35 (3):477-478.
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  24.  5
    A. H. Lachlan (1974). A Note on Thomason's Refined Structures for Tense Logics. Theoria 40 (2):117-120.
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  25. A. H. Lachlan (1967). Review: A. A. Mucnik, E. Mendelson, Isomorphism of Systems of Recursively Enumerable Sets with Effective Properties. [REVIEW] Journal of Symbolic Logic 32 (3):393-394.
     
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  26.  1
    A. H. Lachlan (1964). Effective Operations in a General Setting. Journal of Symbolic Logic 29 (4):163-178.
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  27. Z. Adamowicz, K. Ambos-Spies, A. H. Lachlan, R. I. Soare, R. A. Shore, M. A. da ArchangelskyTaitslin, S. Artemov & J. Bagaria (1994). Master Index to Volumes 61-70. Annals of Pure and Applied Logic 70:289-294.
     
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  28. G. Cherlin, L. Harrington & A. H. Lachlan (1985). Χo-Categorical, Χo-Stable Structures. Annals of Pure and Applied Logic 28 (2):103-135.
     
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  29. M. Hyland Hodges, A. H. Lachlan, A. Louveau, Y. N. Moschovakis, L. Pacholski, A. B. Slomson, J. K. Truss & S. S. Wainer (1998). 1997 European Summer Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 4 (1):55-117.
  30. A. H. Lachlan (1987). A Note on Positive Equivalence Relations. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (1):43-46.
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  31. A. H. Lachlan (1975). A Remark on the Strict Order Property. Mathematical Logic Quarterly 21 (1):69-70.
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  32. A. H. Lachlan (1992). $Aleph_0$-Categorical Tree-Decomposable Structures. Journal of Symbolic Logic 57 (2):501-514.
    Our purpose in this note is to study countable $\aleph_0$-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.
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  33. A. H. Lachlan (1968). Distributive Initial Segments of the Degrees of Unsolvability. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 14 (30):457-472.
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  34. A. H. Lachlan (1962). Multiple Recursion. Mathematical Logic Quarterly 8 (2):81-107.
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  35. A. H. Lachlan (1962). Multiple Recursion. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 8 (2):81-107.
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  36. A. H. Lachlan (1967). On Recursive Enumeration Without Repetition: A Correction. Mathematical Logic Quarterly 13 (7‐12):99-100.
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  37. A. H. Lachlan (1965). On Recursive Enumeration Without Repetition. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 11 (3):209-220.
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  38. A. H. Lachlan (1967). On Recursive Enumeration Without Repetition: A Correction. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 13 (7-12):99-100.
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  39. A. H. Lachlan (1967). Review: J. R. Shoenfield, A Theorem on Minimal Degrees. [REVIEW] Journal of Symbolic Logic 32 (4):529-529.
     
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  40. A. H. Lachlan (1965). Some Notions of Reducibility and Productiveness. Mathematical Logic Quarterly 11 (1):17-44.
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  41. A. H. Lachlan (1965). Some Notions of Reducibility and Productiveness. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 11 (1):17-44.
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  42. A. H. Lachlan (1978). Spectra of Ω-Stable Theories. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (9-11):129-139.
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  43. A. H. Lachlan (1961). TheU-Quantifier. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (11-14):171-174.
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  44. A. H. Lachlan (1961). The U‐Quantifier. Mathematical Logic Quarterly 7 (11‐14):171-174.
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