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.  42
    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.  17
    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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  4. Computable Boolean Algebras.Julia F. Knight & Michael Stob - 2000 - Journal of Symbolic Logic 65 (4):1605-1623.
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  5.  66
    Classification From a Computable Viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
  6. A Complete L Ω1ω-Sentence Characterizing ℵ1.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
  7.  26
    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.
  8.  6
    Coding in Graphs and Linear Orderings.Julia F. Knight, Alexandra A. Soskova & Stefan V. Vatev - 2020 - Journal of Symbolic Logic 85 (2):673-690.
    There is a Turing computable embedding $\Phi $ of directed graphs $\mathcal {A}$ in undirected graphs. Moreover, there is a fixed tuple of formulas that give a uniform effective interpretation; i.e., for all directed graphs $\mathcal {A}$, these formulas interpret $\mathcal {A}$ in $\Phi $. It follows that $\mathcal {A}$ is Medvedev reducible to $\Phi $ uniformly; i.e., $\mathcal {A}\leq _s\Phi $ with a fixed Turing operator that serves for all $\mathcal {A}$. We observe that there is a graph G (...)
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  9.  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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  10.  85
    Barwise: Infinitary Logic and Admissible Sets.H. Jerome Keisler & Julia F. Knight - 2004 - Bulletin of Symbolic Logic 10 (1):4-36.
  11.  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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  12.  70
    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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  13. Hanf Numbers for Omitting Types Over Particular Theories.Julia F. Knight - 1976 - Journal of Symbolic Logic 41 (3):583-588.
  14.  10
    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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  15.  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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  16.  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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  17.  11
    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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  18.  54
    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.  80
    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.
  20. Nonarithmetical ℵ0-Categorical Theories with Recursive Models.Julia F. Knight - 1994 - Journal of Symbolic Logic 59 (1):106 - 112.
  21.  39
    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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  22.  66
    Meeting of the Association for Symbolic Logic: San Antonio, 1987.Julia F. Knight - 1988 - Journal of Symbolic Logic 53 (3):1000-1006.
  23.  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.
  24.  10
    Prime and Atomic Models.Julia F. Knight - 1978 - Journal of Symbolic Logic 43 (3):385-393.
  25.  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.
  26. Meeting of the Association for Symbolic Logic.Julia F. Knight - 1988 - Journal of Symbolic Logic 53 (3):1000-1006.
  27.  7
    Constructions by Transfinitely Many Workers.Julia F. Knight - 1990 - Annals of Pure and Applied Logic 48 (3):237-259.
  28.  32
    In Memoriam: Christopher John Ash.Julia F. Knight - 1995 - Bulletin of Symbolic Logic 1 (2):202.
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  29.  15
    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.
  30.  14
    Additive Structure in Uncountable Models for a Fixed Completion of P.Julia F. Knight - 1983 - Journal of Symbolic Logic 48 (3):623-628.
  31.  21
    Skolem Functions and Elementary Embeddings.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):94-98.
  32.  14
    Saturation of Homogeneous Resplendent Models.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (1):222-224.
  33.  9
    University of California, San Diego, March 20–23, 1999.Julia F. Knight, Steffen Lempp, Toniann Pitassi, Hans Schoutens, Simon Thomas, Victor Vianu & Jindrich Zapletal - 1999 - Bulletin of Symbolic Logic 5 (3).
  34.  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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  35.  9
    Algebraic Independence.Julia F. Knight - 1981 - Journal of Symbolic Logic 46 (2):377-384.
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  36.  8
    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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  37.  12
    Types Omitted in Uncountable Models of Arithmetic.Julia F. Knight - 1975 - Journal of Symbolic Logic 40 (3):317-320.
  38.  22
    Omitting Types in Set Theory and Arithmetic.Julia F. Knight - 1976 - Journal of Symbolic Logic 41 (1):25-32.
  39.  22
    Requirement Systems.Julia F. Knight - 1995 - Journal of Symbolic Logic 60 (1):222-245.
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  40.  5
    Meeting of the Association for Symbolic Logic.Baldwin John, Matt Kaufmann & Julia F. Knight - 1985 - Journal of Symbolic Logic 50 (1):284-286.
  41.  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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  42.  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.
  43.  27
    Minimality and Completions of PA.Julia F. Knight - 2001 - Journal of Symbolic Logic 66 (3):1447-1457.
  44.  5
    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.
  45.  15
    Generic Expansions of Structures.Julia F. Knight - 1973 - Journal of Symbolic Logic 38 (4):561-570.
  46.  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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  47.  4
    Complete Types and the Natural Numbers.Julia F. Knight - 1973 - Journal of Symbolic Logic 38 (3):413-415.
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  48.  14
    A Complete Theory with Arbitrarily Large Minimality Ranks.Robert E. Woodrow & Julia F. Knight - 1983 - 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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  49.  4
    An Inelastic Model with Indiscernibles.Julia F. Knight - 1978 - Journal of Symbolic Logic 43 (2):331-334.
  50.  18
    Degrees of Types and Independent Sequences.Julia F. Knight - 1983 - Journal of Symbolic Logic 48 (4):1074-1081.
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