54 found
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  1.  24
    Degrees Coded in Jumps of Orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
  2.  39
    Isomorphism Relations on Computable Structures.Ekaterina B. Fokina, Sy-David Friedman, Valentina Harizanov, Julia F. Knight, Charles Mccoy & Antonio Montalbán - 2012 - 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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  3.  25
    Π 1 1 Relations and Paths Through.Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Richard A. Shore - 2004 - Journal of Symbolic Logic 69 (2):585-611.
  4. A Complete L Ω1ω-Sentence Characterizing ℵ1.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
  5. Computable Boolean Algebras.Julia F. Knight & Michael Stob - 2000 - Journal of Symbolic Logic 65 (4):1605-1623.
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  6.  15
    Scott Sentences for Certain Groups.Julia F. Knight & Vikram Saraph - 2018 - Archive for Mathematical Logic 57 (3-4):453-472.
    We give Scott sentences for certain computable groups, and we use index set calculations as a way of checking that our Scott sentences are as simple as possible. We consider finitely generated groups and torsion-free abelian groups of finite rank. For both kinds of groups, the computable ones all have computable \ Scott sentences. Sometimes we can do better. In fact, the computable finitely generated groups that we have studied all have Scott sentences that are “computable d-\” sentence and a (...)
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  7.  44
    Computable Trees of Scott Rank [Image] , and Computable Approximation.Wesley Calvert, Julia F. Knight & Jessica Millar - 2006 - 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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  8.  66
    Classification From a Computable Viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
  9.  10
    Computing Strength of Structures Related to the Field of Real Numbers.Gregory Igusa, Julia F. Knight & Noah David Schweber - 2017 - Journal of Symbolic Logic 82 (1):137-150.
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  10.  43
    Decidability and Computability of Certain Torsion-Free Abelian Groups.Rodney G. Downey, Sergei S. Goncharov, Asher M. Kach, Julia F. Knight, Oleg V. Kudinov, Alexander G. Melnikov & Daniel Turetsky - 2010 - 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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  11.  13
    Recursive Structures and Ershov's Hierarchy.Christopher J. Ash & Julia F. Knight - 1996 - 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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  12.  83
    Barwise: Infinitary Logic and Admissible Sets.H. Jerome Keisler & Julia F. Knight - 2004 - Bulletin of Symbolic Logic 10 (1):4-36.
  13.  8
    Turing Computable Embeddings.F. Knight Julia, Miller Sara & M. Vanden Boom - 2007 - 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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  14. Hanf Numbers for Omitting Types Over Particular Theories.Julia F. Knight - 1976 - Journal of Symbolic Logic 41 (3):583-588.
  15.  78
    Simple and Immune Relations on Countable Structures.Sergei S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Charles F. D. McCoy - 2003 - Archive for Mathematical Logic 42 (3):279-291.
  16.  69
    Bounding Prime Models.Barbara F. Csima, Denis R. Hirschfeldt, Julia F. Knight & Robert I. Soare - 2004 - 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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  17.  38
    Chains and Antichains in Partial Orderings.Valentina S. Harizanov, Carl G. Jockusch & Julia F. Knight - 2009 - 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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  18.  53
    Intrinsic Bounds on Complexity and Definability at Limit Levels.John Chisholm, Ekaterina B. Fokina, Sergey S. Goncharov, Valentina S. Harizanov, Julia F. Knight & Sara Quinn - 2009 - 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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  19.  9
    Prime and Atomic Models.Julia F. Knight - 1978 - Journal of Symbolic Logic 43 (3):385-393.
  20.  7
    Constructions by Transfinitely Many Workers.Julia F. Knight - 1990 - Annals of Pure and Applied Logic 48 (3):237-259.
  21.  22
    Requirement Systems.Julia F. Knight - 1995 - Journal of Symbolic Logic 60 (1):222-245.
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  22.  22
    Sequences of N-Diagrams.Valentina S. Harizanov, Julia F. Knight & Andrei S. Morozov - 2002 - Journal of Symbolic Logic 67 (3):1227-1247.
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  23.  27
    Minimality and Completions of PA.Julia F. Knight - 2001 - Journal of Symbolic Logic 66 (3):1447-1457.
  24.  15
    Generic Expansions of Structures.Julia F. Knight - 1973 - Journal of Symbolic Logic 38 (4):561-570.
  25.  9
    Models and Types of Peano's Arithmetic.Haim Gaifman, Julia F. Knight, Fred G. Abramson & Leo A. Harrington - 1983 - Journal of Symbolic Logic 48 (2):484-485.
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  26.  18
    Degrees of Types and Independent Sequences.Julia F. Knight - 1983 - Journal of Symbolic Logic 48 (4):1074-1081.
  27.  8
    A Complete $L{Omega 1omega}$-Sentence Characterizing $Mathbf{Aleph}1$.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
  28.  3
    Spectra of Atomic Theories.Uri Andrews & Julia F. Knight - 2009 - Journal of Symbolic Logic 78 (4):1189-1198.
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  29.  6
    A Completeness Theorem for Certain Classes of Recursive Infinitary Formulas.Christopher J. Ash & Julia F. Knight - 1994 - 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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  30.  14
    Meeting of the Association for Symbolic Logic: Notre Dame, Indiana, 1984.John Baldwin, Matt Kaufmann & Julia F. Knight - 1985 - Journal of Symbolic Logic 50 (1):284-286.
  31.  7
    Representing Scott Sets in Algebraic Settings.Alf Dolich, Julia F. Knight, Karen Lange & David Marker - 2015 - Archive for Mathematical Logic 54 (5-6):631-637.
    We prove that for every Scott set S there are S-saturated real closed fields and S-saturated models of Presburger arithmetic.
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  32.  5
    Uniform Procedures in Uncountable Structures.Noam Greenberg, Alexander G. Melnikov, Julia F. Knight & Daniel Turetsky - 2018 - Journal of Symbolic Logic 83 (2):529-550.
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  33.  5
    Meeting of the Association for Symbolic Logic.Baldwin John, Matt Kaufmann & Julia F. Knight - 1985 - Journal of Symbolic Logic 50 (1):284-286.
  34.  9
    Algebraic Independence.Julia F. Knight - 1981 - Journal of Symbolic Logic 46 (2):377-384.
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  35.  4
    An Inelastic Model with Indiscernibles.Julia F. Knight - 1978 - Journal of Symbolic Logic 43 (2):331-334.
  36.  14
    Additive Structure in Uncountable Models for a Fixed Completion of P.Julia F. Knight - 1983 - Journal of Symbolic Logic 48 (3):623-628.
  37.  3
    Coding in Graphs and Linear Orderings.Julia F. Knight, Alexandra A. Soskova & Stefan V. Vatev - forthcoming - Journal of Symbolic Logic:1-18.
  38.  4
    Complete Types and the Natural Numbers.Julia F. Knight - 1973 - Journal of Symbolic Logic 38 (3):413-415.
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  39.  31
    In Memoriam: Christopher John Ash.Julia F. Knight - 1995 - Bulletin of Symbolic Logic 1 (2):202.
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  40.  17
    Jon Barwise and John Schlipf. An Introduction to Recursively Saturated and Resplendent Models. The Journal of Symbolic Logic, Vol. 41 , Pp. 531–536.Julia F. Knight - 1982 - Journal of Symbolic Logic 47 (2):440.
  41.  16
    John Gregory. Uncountable Models and Infinitary Elementary Extensions. The Journal of Symbolic Logic, Vol. 38 , Pp. 460–470.Julia F. Knight - 1982 - Journal of Symbolic Logic 47 (2):438-439.
  42.  66
    Meeting of the Association for Symbolic Logic: San Antonio, 1987.Julia F. Knight - 1988 - Journal of Symbolic Logic 53 (3):1000-1006.
  43. Meeting of the Association for Symbolic Logic.Julia F. Knight - 1988 - Journal of Symbolic Logic 53 (3):1000-1006.
  44. Nonarithmetical ℵ0-Categorical Theories with Recursive Models.Julia F. Knight - 1994 - Journal of Symbolic Logic 59 (1):106 - 112.
  45.  22
    Omitting Types in Set Theory and Arithmetic.Julia F. Knight - 1976 - Journal of Symbolic Logic 41 (1):25-32.
  46.  6
    Review: Jon Barwise, John Schlipf, An Introduction to Recursively Saturated and Resplendent Models. [REVIEW]Julia F. Knight - 1982 - Journal of Symbolic Logic 47 (2):440-440.
  47.  5
    Review: John Gregory, Uncountable Models and Infinitary Elementary Extensions. [REVIEW]Julia F. Knight - 1982 - Journal of Symbolic Logic 47 (2):438-439.
  48.  4
    Review: J. P. Ressayre, Models with Compactness Properties Relative to an Admissible Language. [REVIEW]Julia F. Knight - 1982 - Journal of Symbolic Logic 47 (2):439-440.
  49.  5
    Ressayre J. P.. Models with Compactness Properties Relative to an Admissible Language. Annals of Mathematical Logic, Vol. 11 No. 1 , Pp. 31–55. [REVIEW]Julia F. Knight - 1982 - Journal of Symbolic Logic 47 (2):439-440.
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  50.  20
    Skolem Functions and Elementary Embeddings.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):94-98.
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