14 found
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  1.  24
    Then-Rea Enumeration Degrees Are Dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
  2.  25
    Some Special Pairs of Σ2 E-Degrees.Seema Ahmad & Alistair H. Lachlan - 1998 - Mathematical Logic Quarterly 44 (4):431-449.
    It is shown that there are incomparable Σ2 e-degrees a, b such that every e-degree strictly less than a is also less than b.
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  3.  2
    ℵ< Sub> 0-Categorical, ℵ< Sub> 0-Stable Structures.Gregory Cherlin, Leo Harrington & Alistair H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
  4.  18
    On the Semantics of the Henkin Quantifier.Michał Krynicki & Alistair H. Lachlan - 1979 - Journal of Symbolic Logic 44 (2):184-200.
  5.  14
    The Continuity of Cupping to 0'.Klaus Ambos-Spies, Alistair H. Lachlan & Robert I. Soare - 1993 - Annals of Pure and Applied Logic 64 (3):195-209.
    It is shown that, if a, b are recursively enumerable degrees such that 0
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  6.  8
    Finite Homogeneous 3‐Graphs.Alistair H. Lachlan & Allyson Tripp - 1995 - Mathematical Logic Quarterly 41 (3):287-306.
  7.  5
    Degrees of Models of True Arithmetic.David Marker, J. Stern, Julia Knight, Alistair H. Lachlan & Robert I. Soare - 1987 - Journal of Symbolic Logic 52 (2):562-563.
  8.  32
    Models of Arithmetic and Upper Bounds for Arithmetic Sets.Alistair H. Lachlan & Robert I. Soare - 1994 - Journal of Symbolic Logic 59 (3):977-983.
    We settle a question in the literature about degrees of models of true arithmetic and upper bounds for the arithmetic sets. We prove that there is a model of true arithmetic whose degree is not a uniform upper bound for the arithmetic sets. The proof involves two forcing constructions.
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  9.  13
    The Priority Method for the Construction of Recursively Enumerable Sets.Alistair H. Lachlan - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 299--310.
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  10.  15
    Two Theorems on Degrees of Models of True Arithmetic.Julia Knight, Alistair H. Lachlan & Robert I. Soare - 1984 - Journal of Symbolic Logic 49 (2):425-436.
  11.  44
    On Countable Homogeneous 3-Hypergraphs.Reza Akhtar & Alistair H. Lachlan - 1995 - Archive for Mathematical Logic 34 (5):331-344.
    We present some results on countable homogeneous 3-hypergraphs. In particular, we show that there is no unexpected homogeneous 3-hypergraph determined by a single constraint.
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  12.  68
    Models of Arithmetic and Subuniform Bounds for the Arithmetic Sets.Alistair H. Lachlan & Robert I. Soare - 1998 - Journal of Symbolic Logic 63 (1):59-72.
    It has been known for more than thirty years that the degree of a non-standard model of true arithmetic is a subuniform upper bound for the arithmetic sets. Here a notion of generic enumeration is presented with the property that the degree of such an enumeration is an suub but not the degree of a non-standard model of true arithmetic. This answers a question posed in the literature.
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  13.  7
    Corrigendum to “The D.R.E. Degrees Are Not Dense” [Ann. Pure Appl. Logic 55 (1991) 125–151].S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 2017 - Annals of Pure and Applied Logic 168 (12):2164-2165.
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  14.  11
    Jump Theorems for REA Operators.Alistair H. Lachlan & Xiaoding Yi - 1993 - Mathematical Logic Quarterly 39 (1):1-6.
    In [2], Jockusch and Shore have introduced a new hierarchy of sets and operators called the REA hierarchy. In this note we prove analogues of the Friedberg Jump Theorem and the Sacks Jump Theorem for many REA operators. MSC: 03D25, 03D55.
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