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Julia F. Knight [60]Julia Knight [21]Julian Knight [1]
  1.  40
    Generic copies of countable structures.Chris Ash, Julia Knight, Mark Manasse & Theodore Slaman - 1989 - Annals of Pure and Applied Logic 42 (3):195-205.
  2.  37
    Degrees coded in jumps of orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
  3.  68
    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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  4.  68
    Enumerations in computable structure theory.Sergey Goncharov, Valentina Harizanov, Julia Knight, Charles McCoy, Russell Miller & Reed Solomon - 2005 - Annals of Pure and Applied Logic 136 (3):219-246.
    We exploit properties of certain directed graphs, obtained from the families of sets with special effective enumeration properties, to generalize several results in computable model theory to higher levels of the hyperarithmetical hierarchy. Families of sets with such enumeration features were previously built by Selivanov, Goncharov, and Wehner. For a computable successor ordinal α, we transform a countable directed graph into a structure such that has a isomorphic copy if and only if has a computable isomorphic copy.A computable structure is (...)
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  5.  29
    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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  6. Computable Boolean algebras.Julia F. Knight & Michael Stob - 2000 - Journal of Symbolic Logic 65 (4):1605-1623.
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  7.  33
    Investigating the Impact of a Musical Intervention on Preschool Children’s Executive Function.Alice Bowmer, Kathryn Mason, Julian Knight & Graham Welch - 2018 - Frontiers in Psychology 9.
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  8.  87
    Classification from a computable viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
    Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence, in terms of relatively simple invariants. Where this is impossible, it is useful to have concrete results saying so. In model theory and descriptive set theory, there is a large body of work showing that certain classes of mathematical structures admit classification while others do not. In the present paper, we (...)
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  9.  50
    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.
  10.  60
    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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  11. A complete L ω1ω-sentence characterizing ℵ1.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
  12.  23
    Computable structures in generic extensions.Julia Knight, Antonio Montalbán & Noah Schweber - 2016 - Journal of Symbolic Logic 81 (3):814-832.
  13.  22
    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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  14.  46
    Models of arithmetic and closed ideals.Julia Knight & Mark Nadel - 1982 - Journal of Symbolic Logic 47 (4):833-840.
  15. Hanf numbers for omitting types over particular theories.Julia F. Knight - 1976 - Journal of Symbolic Logic 41 (3):583-588.
  16.  18
    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.
    In [8], the third author defined a reducibility$\le _w^{\rm{*}}$that lets us compare the computing power of structures of any cardinality. In [6], the first two authors showed that the ordered field of reals${\cal R}$lies strictly above certain related structures. In the present paper, we show that$\left \equiv _w^{\rm{*}}{\cal R}$. More generally, for the weak-looking structure${\cal R}$ℚconsisting of the real numbers with just the ordering and constants naming the rationals, allo-minimal expansions of${\cal R}$ℚare equivalent to${\cal R}$. Using this, we show that (...)
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  17.  93
    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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  18.  21
    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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  19. Barwise: Infinitary logic and admissible sets.H. Jerome Keisler & Julia F. Knight - 2004 - Bulletin of Symbolic Logic 10 (1):4-36.
    §0. Introduction. In [16], Barwise described his graduate study at Stanford. He told of his interactions with Kreisel and Scott, and said how he chose Feferman as his advisor. He began working on admissible fragments of infinitary logic after reading and giving seminar talks on two Ph.D. theses which had recently been completed: that of Lopez-Escobar, at Berkeley, on infinitary logic [46], and that of Platek [58], at Stanford, on admissible sets.Barwise's work on infinitary logic and admissible sets is described (...)
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  20.  18
    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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  21.  32
    Expansions of models and Turing degrees.Julia Knight & Mark Nadel - 1982 - Journal of Symbolic Logic 47 (3):587-604.
  22.  14
    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.  12
    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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  24.  68
    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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  25.  63
    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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  26.  90
    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.
    Let ???? be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of ???? in which the image of R (¬R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on ???? and R, a necessary and sufficient condition for the existence of a computable copy ℬ of ???? in which the image of R (¬R, resp.) (...)
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  27.  12
    Constructions by transfinitely many workers.Julia F. Knight - 1990 - Annals of Pure and Applied Logic 48 (3):237-259.
  28.  27
    Prime and atomic models.Julia F. Knight - 1978 - Journal of Symbolic Logic 43 (3):385-393.
  29.  23
    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.
  30. Nonarithmetical ℵ0-categorical theories with recursive models.Julia F. Knight - 1994 - Journal of Symbolic Logic 59 (1):106 - 112.
  31.  23
    Copying One of a Pair of Structures.Rachael Alvir, Hannah Burchfield & Julia F. Knight - 2022 - Journal of Symbolic Logic 87 (3):1201-1214.
    We ask when, for a pair of structures $\mathcal {A}_1,\mathcal {A}_2$, there is a uniform effective procedure that, given copies of the two structures, unlabeled, always produces a copy of $\mathcal {A}_1$. We give some conditions guaranteeing that there is such a procedure. The conditions might suggest that for the pair of orderings $\mathcal {A}_1$ of type $\omega _1^{CK}$ and $\mathcal {A}_2$ of Harrison type, there should not be any such procedure, but, in fact, there is one. We construct an (...)
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  32.  11
    Interpreting a Field in its Heisenberg Group.Rachael Alvir, Wesley Calvert, Grant Goodman, Valentina Harizanov, Julia Knight, Russell Miller, Andrey Morozov, Alexandra Soskova & Rose Weisshaar - 2022 - Journal of Symbolic Logic 87 (3):1215-1230.
    We improve on and generalize a 1960 result of Maltsev. For a field F, we denote by $H(F)$ the Heisenberg group with entries in F. Maltsev showed that there is a copy of F defined in $H(F)$, using existential formulas with an arbitrary non-commuting pair of elements as parameters. We show that F is interpreted in $H(F)$ using computable $\Sigma _1$ formulas with no parameters. We give two proofs. The first is an existence proof, relying on a result of Harrison-Trainor, (...)
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  33.  16
    Expanding the Reals by Continuous Functions Adds No Computational Power.Uri Andrews, Julia F. Knight, Rutger Kuyper, Joseph S. Miller & Mariya I. Soskova - 2023 - Journal of Symbolic Logic 88 (3):1083-1102.
    We study the relative computational power of structures related to the ordered field of reals, specifically using the notion of generic Muchnik reducibility. We show that any expansion of the reals by a continuous function has no more computing power than the reals, answering a question of Igusa, Knight, and Schweber [7]. On the other hand, we show that there is a certain Borel expansion of the reals that is strictly more powerful than the reals and such that any Borel (...)
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  34.  14
    Spectra of Atomic Theories.Uri Andrews & Julia F. Knight - 2009 - Journal of Symbolic Logic 78 (4):1189-1198.
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  35.  14
    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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  36.  32
    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.
  37.  20
    Erratum to: Limit computable integer parts.Paola D’Aquino, Julia Knight & Karen Lange - 2015 - Archive for Mathematical Logic 54 (3-4):487-489.
  38.  71
    Limit computable integer parts.Paola D’Aquino, Julia Knight & Karen Lange - 2011 - Archive for Mathematical Logic 50 (7-8):681-695.
    Let R be a real closed field. An integer part I for R is a discretely ordered subring such that for every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r \in R}$$\end{document}, there exists an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${i \in I}$$\end{document} so that i ≤ r < i + 1. Mourgues and Ressayre (J Symb Logic 58:641–647, 1993) showed that every real closed field has an integer part. The procedure of Mourgues and (...)
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  39.  16
    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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  40. The Bulletin of Symbolic Logic Volume 11, Number 2, June 2005.Mirna Dzamonja, David M. Evans, Erich Gradel, Geoffrey P. Hellman, Denis Hirschfeldt, Julia Knight, Michael C. Laskowski, Roger Maddux, Volker Peckhaus & Wolfram Pohlers - 2005 - Bulletin of Symbolic Logic 11 (2).
  41.  20
    Phoenix Civic Plaza, Phoenix, Arizona, January 9–10, 2004.Matthew Foreman, Steve Jackson, Julia Knight, R. W. Knight, Steffen Lempp, Françoise Point, Kobi Peterzil, Leonard Schulman, Slawomir Solecki & Carol Wood - 2004 - Bulletin of Symbolic Logic 10 (2).
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  42.  46
    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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  43.  40
    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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  44.  8
    Meeting of the Association for Symbolic Logic.Baldwin John, Matt Kaufmann & Julia F. Knight - 1985 - Journal of Symbolic Logic 50 (1):284-286.
  45.  10
    A Complete $L{omega 1omega}$-Sentence Characterizing $mathbf{aleph}1$.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
  46.  17
    Algebraic independence.Julia F. Knight - 1981 - Journal of Symbolic Logic 46 (2):377-384.
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  47.  12
    An inelastic model with indiscernibles.Julia F. Knight - 1978 - Journal of Symbolic Logic 43 (2):331-334.
  48.  26
    Additive structure in uncountable models for a fixed completion of P.Julia F. Knight - 1983 - Journal of Symbolic Logic 48 (3):623-628.
  49.  18
    books to ASL, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, NY 12604, USA.Julia Knight, Michael C. Laskowski, Roger Maddux, Volker Peckhaus & Wolfram Pohlers - 2004 - Bulletin of Symbolic Logic 10 (3).
  50.  14
    Complete types and the natural numbers.Julia F. Knight - 1973 - Journal of Symbolic Logic 38 (3):413-415.
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