47 found
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  1. Julia F. Knight (1994). Nonarithmetical ℵ0-Categorical Theories with Recursive Models. Journal of Symbolic Logic 59 (1):106 - 112.
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  2. Julia F. Knight (1977). A Complete Lω 1ω-Sentence Characterizing ℵ. Journal of Symbolic Logic 42 (1):59 - 62.
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  3. Julia F. Knight (1976). Hanf Numbers for Omitting Types Over Particular Theories. Journal of Symbolic Logic 41 (3):583-588.
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  4. Julia F. Knight & Michael Stob (2000). Computable Boolean Algebras. Journal of Symbolic Logic 65 (4):1605-1623.
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  5.  53
    Julia F. Knight (1988). Meeting of the Association for Symbolic Logic: San Antonio, 1987. Journal of Symbolic Logic 53 (3):1000-1006.
  6.  13
    Ekaterina B. Fokina, Sy-David Friedman, Valentina Harizanov, Julia F. Knight, Charles McCoy & Antonio Montalbán (2012). Isomorphism Relations on Computable Structures. Journal of Symbolic Logic 77 (1):122-132.
    We study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all ${\mathrm{\Sigma }}_{1}^{1}$ equivalence relations on hyperarithmetical subsets of ω.
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  7.  9
    Rodney G. Downey, Sergei S. Goncharov, Asher M. Kach, Julia F. Knight, Oleg V. Kudinov, Alexander G. Melnikov & Daniel Turetsky (2010). Decidability and Computability of Certain Torsion-Free Abelian Groups. Notre Dame Journal of Formal Logic 51 (1):85-96.
    We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.
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  8.  7
    Julia F. Knight (1986). Degrees Coded in Jumps of Orderings. Journal of Symbolic Logic 51 (4):1034-1042.
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  9.  23
    Valentina S. Harizanov, Carl G. Jockusch Jr & Julia F. Knight (2009). Chains and Antichains in Partial Orderings. Archive for Mathematical Logic 48 (1):39-53.
    We study the complexity of infinite chains and antichains in computable partial orderings. We show that there is a computable partial ordering which has an infinite chain but none that is ${\Sigma _{1}^{1}}$ or ${\Pi _{1}^{1}}$ , and also obtain the analogous result for antichains. On the other hand, we show that every computable partial ordering which has an infinite chain must have an infinite chain that is the difference of two ${\Pi _{1}^{1}}$ sets. Our main result is that there (...)
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  10.  18
    Wesley Calvert & Julia F. Knight (2006). Classification From a Computable Viewpoint. Bulletin of Symbolic Logic 12 (2):191-218.
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  11.  24
    H. Jerome Keisler & Julia F. Knight (2004). Barwise: Infinitary Logic and Admissible Sets. Bulletin of Symbolic Logic 10 (1):4-36.
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  12.  7
    Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Richard A. Shore (2004). Π 1 1 Relations and Paths Through. Journal of Symbolic Logic 69 (2):585-611.
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  13.  8
    Sergei S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Charles F. D. McCoy (2003). Simple and Immune Relations on Countable Structures. Archive for Mathematical Logic 42 (3):279-291.
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  14.  1
    Christopher J. Ash & Julia F. Knight (1996). Recursive Structures and Ershov's Hierarchy. Mathematical Logic Quarterly 42 (1):461-468.
    Ash and Nerode [2] gave natural definability conditions under which a relation is intrinsically r. e. Here we generalize this to arbitrary levels in Ershov's hierarchy of Δmath image sets, giving conditions under which a relation is intrinsically α-r. e.
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  15.  11
    Julia F. Knight (1995). Requirement Systems. Journal of Symbolic Logic 60 (1):222-245.
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  16.  9
    John Baldwin, Matt Kaufmann & Julia F. Knight (1985). Meeting of the Association for Symbolic Logic: Notre Dame, Indiana, 1984. Journal of Symbolic Logic 50 (1):284-286.
  17.  8
    Julia F. Knight (1983). Additive Structure in Uncountable Models for a Fixed Completion of P. Journal of Symbolic Logic 48 (3):623-628.
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  18.  11
    Julia F. Knight (1983). Degrees of Types and Independent Sequences. Journal of Symbolic Logic 48 (4):1074-1081.
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  19.  3
    Julia F. Knight (1973). Complete Types and the Natural Numbers. Journal of Symbolic Logic 38 (3):413-415.
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  20.  2
    Julia F. Knight (1990). Constructions by Transfinitely Many Workers. Annals of Pure and Applied Logic 48 (3):237-259.
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  21.  15
    Julia F. Knight (1995). In Memoriam: Christopher John Ash. Bulletin of Symbolic Logic 1 (2):202.
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  22.  2
    Alf Dolich, Julia F. Knight, Karen Lange & David Marker (2015). Representing Scott Sets in Algebraic Settings. Archive for Mathematical Logic 54 (5-6):631-637.
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  23.  15
    John Chisholm, Ekaterina B. Fokina, Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Sara Quinn (2009). Intrinsic Bounds on Complexity and Definability at Limit Levels. Journal of Symbolic Logic 74 (3):1047-1060.
    We show that for every computable limit ordinal α, there is a computable structure A that is $\Delta _\alpha ^0 $ categorical, but not relatively $\Delta _\alpha ^0 $ categorical (equivalently. it does not have a formally $\Sigma _\alpha ^0 $ Scott family). We also show that for every computable limit ordinal a, there is a computable structure A with an additional relation R that is intrinsically $\Sigma _\alpha ^0 $ on A. but not relatively intrinsically $\Sigma _\alpha ^0 $ (...)
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  24.  15
    Valentina S. Harizanov, Julia F. Knight & Andrei S. Morozov (2002). Sequences of N-Diagrams. Journal of Symbolic Logic 67 (3):1227-1247.
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  25.  4
    Robert E. Woodrow & Julia F. Knight (1983). A Complete Theory with Arbitrarily Large Minimality Ranks. Journal of Symbolic Logic 48 (2):321-328.
    An example is given of a complete theory with minimal models of arbitrarily large minimality rank.
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  26.  8
    Barbara F. Csima, Denis R. Hirschfeldt, Julia F. Knight & Robert I. Soare (2004). Bounding Prime Models. Journal of Symbolic Logic 69 (4):1117 - 1142.
    A set X is prime bounding if for every complete atomic decidable (CAD) theory T there is a prime model U of T decidable in X. It is easy to see that $X = 0\prime$ is prime bounding. Denisov claimed that every $X <_{T} 0\prime$ is not prime bounding, but we discovered this to be incorrect. Here we give the correct characterization that the prime bounding sets $X \leq_{T} 0\prime$ are exactly the sets which are not $low_2$ . Recall that (...)
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  27.  2
    Christopher J. Ash & Julia F. Knight (1994). A Completeness Theorem for Certain Classes of Recursive Infinitary Formulas. Mathematical Logic Quarterly 40 (2):173-181.
    We consider the following generalization of the notion of a structure recursive relative to a set X. A relational structure A is said to be a Γ-structure if for each relation symbol R, the interpretation of R in A is ∑math image relative to X, where β = Γ. We show that a certain, fairly obvious, description of classes ∑math image of recursive infinitary formulas has the property that if A is a Γ-structure and S is a further relation on (...)
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  28.  2
    John Baldwin, Johanna Ny Franklin, C. Ward Henson, Julia F. Knight, Roman Kossak, Dima Sinapova, W. Hugh Woodin & Philip Scowcroft (2013). John B. Hynes Veterans Memorial Convention Center Boston Marriott Hotel, and Boston Sheraton Hotel Boston, MA January 6–7, 2012. [REVIEW] Bulletin of Symbolic Logic 19 (2).
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  29.  3
    Julia F. Knight (1973). Generic Expansions of Structures. Journal of Symbolic Logic 38 (4):561-570.
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  30.  3
    Julia F. Knight (1981). Algebraic Independence. Journal of Symbolic Logic 46 (2):377-384.
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  31.  5
    Julia F. Knight (1986). Saturation of Homogeneous Resplendent Models. Journal of Symbolic Logic 51 (1):222-224.
  32.  7
    Julia F. Knight (1977). Skolem Functions and Elementary Embeddings. Journal of Symbolic Logic 42 (1):94-98.
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  33.  2
    Julia F. Knight (1982). Review: Jon Barwise, John Schlipf, An Introduction to Recursively Saturated and Resplendent Models. [REVIEW] Journal of Symbolic Logic 47 (2):440-440.
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  34.  2
    Julia F. Knight (1978). An Inelastic Model with Indiscernibles. Journal of Symbolic Logic 43 (2):331-334.
  35.  1
    Julia F. Knight (1976). Omitting Types in Set Theory and Arithmetic. Journal of Symbolic Logic 41 (1):25-32.
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  36.  3
    Julia F. Knight (1978). Prime and Atomic Models. Journal of Symbolic Logic 43 (3):385-393.
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  37.  5
    Julia F. Knight (2001). Minimality and Completions of PA. Journal of Symbolic Logic 66 (3):1447-1457.
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  38.  4
    Julia F. Knight (1975). Types Omitted in Uncountable Models of Arithmetic. Journal of Symbolic Logic 40 (3):317-320.
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  39.  1
    Julia F. Knight (1982). Review: J.-P. Ressayre, Boolean Models and Infinitary First Order Languages. [REVIEW] Journal of Symbolic Logic 47 (2):439-439.
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  40.  1
    Julia F. Knight (1982). Review: John Gregory, Uncountable Models and Infinitary Elementary Extensions. [REVIEW] Journal of Symbolic Logic 47 (2):438-439.
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  41.  1
    Sergei S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Charles F. D. McCoy (2003). Simple and Immune Relations on Countable Structures. Archive for Mathematical Logic 42 (3):279-291.
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  42.  1
    Julia F. Knight (1982). Review: J. P. Ressayre, Models with Compactness Properties Relative to an Admissible Language. [REVIEW] Journal of Symbolic Logic 47 (2):439-440.
  43.  2
    Wesley Calvert, Julia F. Knight & Jessica Millar (2006). Computable Trees of Scott Rank [Image] , and Computable Approximation. Journal of Symbolic Logic 71 (1):283 - 298.
    Makkai [10] produced an arithmetical structure of Scott rank $\omega _{1}^{\mathit{CK}}$. In [9]. Makkai's example is made computable. Here we show that there are computable trees of Scott rank $\omega _{1}^{\mathit{CK}}$. We introduce a notion of "rank homogeneity". In rank homogeneous trees, orbits of tuples can be understood relatively easily. By using these trees, we avoid the need to pass to the more complicated "group trees" of [10] and [9]. Using the same kind of trees, we obtain one of rank (...)
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  44.  2
    Julia F. Knight, Sara Miller & M. Vanden Boom (2007). Turing Computable Embeddings. Journal of Symbolic Logic 72 (3):901-918.
    In [3], two different effective versions of Borel embedding are defined. The first, called computable embedding, is based on uniform enumeration reducibility, while the second, called Turing computable embedding, is based on uniform Turing reducibility. While [3] focused mainly on computable embeddings, the present paper considers Turing computable embeddings. Although the two notions are not equivalent, we can show that they behave alike on the mathematically interesting classes chosen for investigation in [3]. We give a “Pull-back Theorem”, saying that if (...)
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  45. Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Richard A. Shore (2004). Π11 Relations and Paths Through. Journal of Symbolic Logic 69 (2):585-611.
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  46. Julia F. Knight (1977). A Complete $L{Omega 1omega}$-Sentence Characterizing $Mathbf{Aleph}1$. Journal of Symbolic Logic 42 (1):59-62.
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  47. Julia F. Knight, Steffen Lempp, Toniann Pitassi, Hans Schoutens, Simon Thomas, Victor Vianu & Jindrich Zapletal (1999). University of California, San Diego, March 20–23, 1999. Bulletin of Symbolic Logic 5 (3).
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