48 found
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  1.  37
    ℵ0-Categorical, ℵ0-Stable Structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
  2.  51
    On Strongly Minimal Sets.J. T. Baldwin & A. H. Lachlan - 1971 - Journal of Symbolic Logic 36 (1):79-96.
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  3.  19
    Distributive Initial Segments of the Degrees of Unsolvability.A. H. Lachlan - 1968 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 14 (30):457-472.
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  4.  20
    Bounding Minimal Pairs.A. H. Lachlan - 1979 - Journal of Symbolic Logic 44 (4):626-642.
  5.  1
    Distributive Initial Segments of the Degrees of Unsolvability.A. H. Lachlan - 1968 - Mathematical Logic Quarterly 14 (30):457-472.
  6.  16
    A Note on Positive Equivalence Relations.A. H. Lachlan - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (1):43-46.
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  7. A Note on Positive Equivalence Relations.A. H. Lachlan - 1987 - Mathematical Logic Quarterly 33 (1):43-46.
  8.  9
    J. R. Shoenfield. A Theorem on Minimal Degrees. The Journal of Symbolic Logic, Vol. 31 , Pp. 539–544.A. H. Lachlan - 1968 - Journal of Symbolic Logic 32 (4):529.
  9.  21
    Countable Initial Segments of the Degrees of Unsolvability.A. H. Lachlan & R. Lebeuf - 1976 - Journal of Symbolic Logic 41 (2):289-300.
  10.  19
    Spectra of Ω-Stable Theories.A. H. Lachlan - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (9-11):129-139.
  11.  5
    Degrees of Recursively Enumerable Sets Which Have No Maximal Supersets.A. H. Lachlan - 1968 - Journal of Symbolic Logic 33 (3):431-443.
  12.  6
    Spectra of Ω‐Stable Theories.A. H. Lachlan - 1978 - Mathematical Logic Quarterly 24 (9‐11):129-139.
  13.  28
    On the Indexing of Classes of Recursively Enumerable Sets.A. H. Lachlan - 1966 - Journal of Symbolic Logic 31 (1):10-22.
  14.  15
    The Impossibility of Finding Relative Complements for Recursively Enumerable Degrees.A. H. Lachlan - 1966 - Journal of Symbolic Logic 31 (3):434-454.
  15.  23
    Standard Classes of Recursively Enumerable Sets.A. H. Lachlan - 1964 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 10 (2-3):23-42.
  16. Master Index to Volumes 61-70.Z. Adamowicz, K. Ambos-Spies, A. H. Lachlan, R. I. Soare, R. A. Shore, M. A. da ArchangelskyTaitslin, S. Artemov & J. Bagaria - 1994 - Annals of Pure and Applied Logic 70:289-294.
     
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  17.  19
    Some Notions of Reducibility and Productiveness.A. H. Lachlan - 1965 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 11 (1):17-44.
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  18.  22
    On Recursive Enumeration Without Repetition.A. H. Lachlan - 1965 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 11 (3):209-220.
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  19.  27
    On Recursive Enumeration Without Repetition: A Correction.A. H. Lachlan - 1967 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 13 (7-12):99-100.
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  20.  4
    Countable Models of ℵ 1 -Categorical Theories.Michael Morley, J. T. Baldwin & A. H. Lachlan - 1975 - Journal of Symbolic Logic 40 (4):636-637.
  21.  5
    On the Number of Countable Models of a Countable Superstable Theory.A. H. Lachlan, Patrick Suppes & Daniel Lascar - 1982 - Journal of Symbolic Logic 47 (1):215-217.
  22.  22
    On Recursive Enumeration Without Repetition.A. H. Lachlan - 1965 - Mathematical Logic Quarterly 11 (3):209-220.
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  23.  12
    Some Notions of Reducibility and Productiveness.A. H. Lachlan - 1965 - Mathematical Logic Quarterly 11 (1):17-44.
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  24.  9
    Structures Coordinatized by Indiscernible Sets.A. H. Lachlan - 1987 - Annals of Pure and Applied Logic 34 (3):245-273.
  25.  49
    A Note on Thomason's Refined Structures for Tense Logics.A. H. Lachlan - 1974 - Theoria 40 (2):117-120.
  26.  12
    A Note on Thomason's Refined Structures for Tense Logics.A. H. Lachlan, Kit Fine, Stig Kanger, R. I. Goldblatt, S. K. Thomason & J. N. Crossley - 1982 - Journal of Symbolic Logic 47 (2):440-445.
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  27.  22
    Multiple Recursion.A. H. Lachlan - 1962 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 8 (2):81-107.
  28.  8
    A Remark on the Strict Order Property.A. H. Lachlan - 1975 - Mathematical Logic Quarterly 21 (1):69-70.
  29.  15
    Some Coinductive Graphs.A. H. Lachlan - 1990 - 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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  30.  21
    TheU-Quantifier.A. H. Lachlan - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (11-14):171-174.
  31.  26
    Complete Theories with Only Universal and Existential Axioms.A. H. Lachlan - 1987 - 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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  32.  15
    A Note on Universal Sets.A. H. Lachlan - 1966 - Journal of Symbolic Logic 31 (4):573-574.
  33.  17
    Uniform Enumeration Operations.A. H. Lachlan - 1975 - 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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  34.  10
    On Recursive Enumeration Without Repetition: A Correction.A. H. Lachlan - 1967 - Mathematical Logic Quarterly 13 (7‐12):99-100.
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  35.  9
    Recursively Enumerable Classes and Their Application to Recursive Sequences of Formal Theories.Marian Boykan Pour-el, Hilary Putnam, William A. Howard & A. H. Lachlan - 1973 - Journal of Symbolic Logic 38 (1):155-156.
  36.  27
    ℵ0-Categorical Tree-Decomposable Structures.A. H. Lachlan - 1992 - 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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  37.  10
    Recursive Real Numbers.A. H. Lachlan - 1963 - Journal of Symbolic Logic 28 (1):1-16.
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  38.  12
    Effective Operations in a General Setting.A. H. Lachlan - 1964 - Journal of Symbolic Logic 29 (4):163-178.
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  39.  6
    $Aleph_0$-Categorical Tree-Decomposable Structures.A. H. Lachlan - 1992 - 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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  40.  6
    The U‐Quantifier.A. H. Lachlan - 1961 - Mathematical Logic Quarterly 7 (11‐14):171-174.
  41.  3
    Review: Paul R. Young, An Effective Operator, Continuous but Not Partial Recursive. [REVIEW]A. H. Lachlan - 1970 - Journal of Symbolic Logic 35 (3):477-478.
  42. Review: A. A. Mucnik, E. Mendelson, Isomorphism of Systems of Recursively Enumerable Sets with Effective Properties. [REVIEW]A. H. Lachlan - 1967 - Journal of Symbolic Logic 32 (3):393-394.
  43.  2
    Mučnik A. A.. Izomorfizm Sistém Rékursivno Péréčislimyh Množéstv s Efféktivnymi Svojstvami. Trudy Moskovskogo Matématičéskogo Obščéstva, Vol. 7 , Pp. 407–412.Mučnik A. A.. Isomorphism of Systems of Recursively Enumerable Sets with Effective Properties. English Translation of the Preceding by Mendelson E.. American Mathematical Society Translations, Ser. 2 Vol. 23 , Pp. 7–13. [REVIEW]A. H. Lachlan - 1967 - Journal of Symbolic Logic 32 (3):393-394.
  44.  2
    Young Paul R.. An Effective Operator, Continuous but Not Partial Recursive. Proceedings of the American Mathematical Society, Vol. 19 , Pp. 103–108. [REVIEW]A. H. Lachlan - 1970 - Journal of Symbolic Logic 35 (3):477-478.
  45.  2
    1997 European Summer Meeting of the Association for Symbolic Logic.M. Hyland Hodges, A. H. Lachlan, A. Louveau, Y. N. Moschovakis, L. Pacholski, A. B. Slomson, J. K. Truss & S. S. Wainer - 1998 - Bulletin of Symbolic Logic 4 (1):55-117.
  46.  1
    Multiple Recursion.A. H. Lachlan - 1962 - Mathematical Logic Quarterly 8 (2):81-107.
  47. Review: J. R. Shoenfield, A Theorem on Minimal Degrees. [REVIEW]A. H. Lachlan - 1967 - Journal of Symbolic Logic 32 (4):529-529.
  48.  11
    Simplicity of Recursively Enumerable Sets.Two Theorems on Hyperhypersimple Sets.On the Lattice of Recursively Enumerable Sets.The Elementary Theory of Recursively Enumerable Sets.Robert W. Robinson & A. H. Lachlan - 1970 - Journal of Symbolic Logic 35 (1):153-155.