Results for 'Lachlan Doughney'

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Lachlan Doughney
University of Melbourne
  1. Ayn Rand and Deducing 'Ought' From 'Is'.Lachlan Doughney - 2012 - Journal of Ayn Rand Studies 12 (1):151-168.
    The article discusses how and why philosopher Ayn Rand attempted to deduce an ought conclusion from only is premises. It contends that Rand did attempt to deduce what one ought and ought not do from what is or is not the case. It argues that Rand attempted to provide a universally objective unshakable normative moral claim, that people ought to act in accordance with her value and virtue system.
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  2.  46
    ℵ0-Categorical, ℵ0-Stable Structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
  3.  5
    A Recursively Enumerable Degree Which Will Not Split Over All Lesser Ones.Alistair H. Lachlan - 1976 - Annals of Pure and Applied Logic 9 (4):307.
  4.  58
    On Strongly Minimal Sets.J. T. Baldwin & A. H. Lachlan - 1971 - Journal of Symbolic Logic 36 (1):79-96.
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  5.  19
    The D.R.E. Degrees Are Not Dense.S. Cooper, Leo Harrington, Alistair Lachlan, Steffen Lempp & Robert Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
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  6.  18
    Then-Rea Enumeration Degrees Are Dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
  7.  22
    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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  8.  23
    Bounding Minimal Pairs.A. H. Lachlan - 1979 - Journal of Symbolic Logic 44 (4):626-642.
  9.  4
    Initial Segments of Models of Peano's Axioms.L. A. S. Kirby, J. B. Paris, A. Lachlan, M. Srebrny & A. Zarach - 1983 - Journal of Symbolic Logic 48 (2):482-483.
  10.  19
    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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  11.  1
    Distributive Initial Segments of the Degrees of Unsolvability.A. H. Lachlan - 1968 - Mathematical Logic Quarterly 14 (30):457-472.
  12. Is Innovation in Bird Song Adaptive?Peter J. B. Slater & Robert F. Lachlan - 2003 - In Simon M. Reader & Kevin N. Laland (eds.), Animal Innovation. Oxford University Press.
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  13.  3
    A Note on Positive Equivalence Relations.A. H. Lachlan - 1987 - Mathematical Logic Quarterly 33 (1):43-46.
  14.  22
    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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  15.  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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  16.  12
    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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  17.  21
    Vector Spaces and Binary Quantifiers.Michał Krynicki, Alistair Lachlan & Jouko Väänänen - 1984 - Notre Dame Journal of Formal Logic 25 (1):72-78.
  18.  22
    Countable Initial Segments of the Degrees of Unsolvability.A. H. Lachlan & R. Lebeuf - 1976 - Journal of Symbolic Logic 41 (2):289-300.
  19.  22
    Spectra of Ω-Stable Theories.A. H. Lachlan - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (9-11):129-139.
  20.  7
    Finite Homogeneous 3‐Graphs.Alistair H. Lachlan & Allyson Tripp - 1995 - Mathematical Logic Quarterly 41 (3):287-306.
  21.  18
    On the Semantics of the Henkin Quantifier.Michał Krynicki & Alistair H. Lachlan - 1979 - Journal of Symbolic Logic 44 (2):184-200.
  22.  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.
  23.  7
    Degrees of Recursively Enumerable Sets Which Have No Maximal Supersets.A. H. Lachlan - 1968 - Journal of Symbolic Logic 33 (3):431-443.
  24.  7
    Spectra of Ω‐Stable Theories.A. H. Lachlan - 1978 - Mathematical Logic Quarterly 24 (9‐11):129-139.
  25.  17
    The Impossibility of Finding Relative Complements for Recursively Enumerable Degrees.A. H. Lachlan - 1966 - Journal of Symbolic Logic 31 (3):434-454.
  26.  30
    On the Indexing of Classes of Recursively Enumerable Sets.A. H. Lachlan - 1966 - Journal of Symbolic Logic 31 (1):10-22.
  27.  12
    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.
  28.  35
    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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  29.  23
    Standard Classes of Recursively Enumerable Sets.A. H. Lachlan - 1964 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 10 (2-3):23-42.
  30. 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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  31.  28
    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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  32.  20
    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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  33.  26
    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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  34.  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.
  35.  5
    Countable Models of ℵ 1 -Categorical Theories.Michael Morley, J. T. Baldwin & A. H. Lachlan - 1975 - Journal of Symbolic Logic 40 (4):636-637.
  36.  29
    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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  37.  23
    On Recursive Enumeration Without Repetition.A. H. Lachlan - 1965 - Mathematical Logic Quarterly 11 (3):209-220.
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  38.  13
    Some Notions of Reducibility and Productiveness.A. H. Lachlan - 1965 - Mathematical Logic Quarterly 11 (1):17-44.
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  39.  10
    Structures Coordinatized by Indiscernible Sets.A. H. Lachlan - 1987 - Annals of Pure and Applied Logic 34 (3):245-273.
  40.  49
    A Note on Thomason's Refined Structures for Tense Logics.A. H. Lachlan - 1974 - Theoria 40 (2):117-120.
  41.  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.
  42.  12
    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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  43.  9
    A Remark on the Strict Order Property.A. H. Lachlan - 1975 - Mathematical Logic Quarterly 21 (1):69-70.
  44.  27
    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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  45.  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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  46.  23
    Multiple Recursion.A. H. Lachlan - 1962 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 8 (2):81-107.
  47.  16
    A Note on Universal Sets.A. H. Lachlan - 1966 - Journal of Symbolic Logic 31 (4):573-574.
    In this note is proved the following:Theorem.Iƒ A × B is universal and one oƒ A, B is r.e. then one of A, B is universal.Letα, τbe 1-argument recursive functions such thatxgoes to, τ) is a map of the natural numbers onto all ordered pairs of natural numbers. A set A of natural numbers is calleduniversalif every r.e. set is reducible to A; A × B is calleduniversalif the set.
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  48.  19
    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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  49. Ω-Categorical, Ω-Stable Structures.G. Cherlin, L. Harrington & A. Lachlan - 1986 - Annals of Pure and Applied Logic 18:227-70.
  50.  21
    TheU-Quantifier.A. H. Lachlan - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (11-14):171-174.
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