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  1. Seema Ahmad & Alistair H. Lachlan (1998). Some Special Pairs of Σ2 E-Degrees. 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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  2. Alistair H. Lachlan & Robert I. Soare (1998). Models of Arithmetic and Subuniform Bounds for the Arithmetic Sets. 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 (suub). 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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  3. Reza Akhtar & Alistair H. Lachlan (1995). On Countable Homogeneous 3-Hypergraphs. 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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  4. Alistair H. Lachlan & Allyson Tripp (1995). Finite Homogeneous 3‐Graphs. Mathematical Logic Quarterly 41 (3):287-306.
    By “3-graph” we mean a pair such that E ⊆ [V]3. We show that the only non-trivial finite 3-graphs homogeneous in the sense of Fraïssé are those associated with the projective planes over GF and GF, and with the projective lines over GF and GF. To exclude other possibilities we use the classification of doubly transitive finite permutation groups.
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  5. Alistair H. Lachlan & Robert I. Soare (1994). Models of Arithmetic and Upper Bounds for Arithmetic Sets. 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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  6. Klaus Ambos-Spies, Alistair H. Lachlan & Robert I. Soare (1993). The Continuity of Cupping to 0'. 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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  7. Alistair H. Lachlan & Xiaoding Yi (1993). Jump Theorems for REA Operators. 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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  8. Alistair H. Lachlan & Richard A. Shore (1992). Then-Rea Enumeration Degrees Are Dense. Archive for Mathematical Logic 31 (4):277-285.
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  9. Akira Kanda & Alistair H. Lachlan (1987). Alternative Characterizations of Precomplete Numerations. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (2):97-100.
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  10. David Marker, J. Stern, Julia Knight, Alistair H. Lachlan & Robert I. Soare (1987). Degrees of Models of True Arithmetic. Journal of Symbolic Logic 52 (2):562-563.
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  11. Gregory Cherlin, Leo Harrington & Alistair H. Lachlan (1985). ℵ< Sub> 0-Categorical, ℵ< Sub> 0-Stable Structures. Annals of Pure and Applied Logic 28 (2):103-135.
     
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  12. Julia Knight, Alistair H. Lachlan & Robert I. Soare (1984). Two Theorems on Degrees of Models of True Arithmetic. Journal of Symbolic Logic 49 (2):425-436.
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  13. Michał Krynicki & Alistair H. Lachlan (1979). On the Semantics of the Henkin Quantifier. Journal of Symbolic Logic 44 (2):184-200.
  14. Alistair H. Lachlan (1976). A Recursively Enumerable Degree Which Will Not Split Over All Lesser Ones. Annals of Mathematical Logic 9 (4):307-365.
  15. Alistair H. Lachlan (1973). The Priority Method for the Construction of Recursively Enumerable Sets. In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York,Springer-Verlag. 299--310.
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