6 found
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  1.  28
    Index Sets for Classes of High Rank Structures.W. Calvert, E. Fokina, S. S. Goncharov, J. F. Knight, O. Kudinov, A. S. Morozov & V. Puzarenko - 2007 - Journal of Symbolic Logic 72 (4):1418 - 1432.
    This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O.
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  2.  39
    Categoricity of Computable Infinitary Theories.W. Calvert, S. S. Goncharov, J. F. Knight & Jessica Millar - 2009 - Archive for Mathematical Logic 48 (1):25-38.
    Computable structures of Scott rank ${\omega_1^{CK}}$ are an important boundary case for structural complexity. While every countable structure is determined, up to isomorphism, by a sentence of ${\mathcal{L}_{\omega_1 \omega}}$ , this sentence may not be computable. We give examples, in several familiar classes of structures, of computable structures with Scott rank ${\omega_1^{CK}}$ whose computable infinitary theories are each ${\aleph_0}$ -categorical. General conditions are given, covering many known methods for constructing computable structures with Scott rank ${\omega_1^{CK}}$ , which guarantee that the (...)
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  3.  35
    Decidable Boolean Algebras of Low Level.S. S. Goncharov - 1998 - Annals of Pure and Applied Logic 94 (1-3):75-95.
    We will study the question about decidability for Boolean algebras with first elementary characteristic one. The main problem is sufficient conditions for decidability of Boolean algebras with recursive representation for extended signature by definable predicates. We will use the base definitions on recursive and constructive models from [2, 4–6, 10, 11] but on Boolean algebras from [1, 8].
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  4.  44
    Axiomatizable Classes with Strong Homomorphisms.S. S. Goncharov - 1987 - Studia Logica 46 (2):113 - 120.
    In the paper A. I. Malcev's problem on the characterization of axioms for classes with strong homomorphisms is being solved.
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  5.  15
    Hanf Number for Scott Sentences of Computable Structures.S. S. Goncharov, J. F. Knight & I. Souldatos - 2018 - Archive for Mathematical Logic 57 (7-8):889-907.
    The Hanf number for a set S of sentences in \ is the least infinite cardinal \ such that for all \, if \ has models in all infinite cardinalities less than \, then it has models of all infinite cardinalities. Friedman asked what is the Hanf number for Scott sentences of computable structures. We show that the value is \. The same argument proves that \ is the Hanf number for Scott sentences of hyperarithmetical structures.
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  6. Morley's Problem.S. S. Goncharov - 1997 - Bulletin of Symbolic Logic 3:99.