Results for 'Mikhail Peretyat'kin'

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  1.  24
    The Lindenbaum Algebra of the Theory of the Class of All Finite Models.Steffen Lempp, Mikhail Peretyat'kin & Reed Solomon - 2002 - Journal of Mathematical Logic 2 (02):145-225.
    In this paper, we investigate the Lindenbaum algebra ℒ of the theory T fin = Th of the class M fin of all finite models of a finite rich signature. We prove that this algebra is an atomic Boolean algebra while its Gödel numeration γ is a [Formula: see text]-numeration. Moreover, the quotient algebra /ℱ, γ/ℱ) modulo the Fréchet ideal ℱ is a [Formula: see text]-algebra, which is universal over the class of all [Formula: see text] Boolean algebras. These conditions (...)
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  2.  23
    Mikhail G. Peretyat'Kin. Konechno Aksiomatiziruemye Teorii. Russian Original of the Preceding. Sibirskaya Shkola Algebry I Logiki. Nauchnaya Kniga, Novosibirsk1997, 322 + Xiv Pp. - F. R. Drake and D. Singh. Intermediate Set Theory. John Wiley & Sons, Chichester, New York, Etc., 1996, X + 234 Pp. - Winfried Just and Martin Weese. Discovering Modern Set Theory. II. Set-Theoretic Tools for Every Mathematician. Graduate Studies in Mathematics, Vol. 18. American Mathematical Society, Providence1997, Xiii + 224 Pp. [REVIEW]Martin Goldstern - 1999 - Journal of Symbolic Logic 64 (4):1830-1832.
  3.  18
    Mikhail G. Peretyat'Kin. Finitely Axiomatizable Theories. English Translation of Konechno Aksiomatiziruemye Teorii. Siberian School of Algebra and Logic. Consultants Bureau, New York, London, and Moscow, 1977, Xiv + 294 Pp. [REVIEW]Vivienne Morley - 1999 - Journal of Symbolic Logic 64 (4):1828-1830.
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    Review: Mikhail G. Peretyat'kin, Finitely Axiomatizable Theories. [REVIEW]Vivienne Morley - 1999 - Journal of Symbolic Logic 64 (4):1828-1830.
  5.  10
    Review: Mikhail G. Peretyat'kin, Konechno Aksiomatiziruemye Teorii; F. R. Drake, D. Singh, Intermediate Set Theory; Winfried Just, Martin Weese, Discovering Modern Set Theory. II. Set-Theoretic Tools for Every Mathematician. [REVIEW]Martin Goldstern - 1999 - Journal of Symbolic Logic 64 (4):1830-1832.
  6.  3
    On the Tarski-Lindenbaum Algebra of the Class of All Strongly Constructivizable Prime Models.Mikhail G. Peretyat’kin - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 589--598.
  7.  19
    Computability of Homogeneous Models.Karen Lange & Robert I. Soare - 2007 - Notre Dame Journal of Formal Logic 48 (1):143-170.
    In the last five years there have been a number of results about the computable content of the prime, saturated, or homogeneous models of a complete decidable theory T in the spirit of Vaught's "Denumerable models of complete theories" combined with computability methods for degrees d ≤ 0′. First we recast older results by Goncharov, Peretyat'kin, and Millar in a more modern framework which we then apply. Then we survey recent results by Lange, "The degree spectra of homogeneous models," (...)
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  8.  7
    A Characterization of the 0 -Basis Homogeneous Bounding Degrees.Karen Lange - 2010 - Journal of Symbolic Logic 75 (3):971-995.
    We say a countable model has a 0-basis if the types realized in are uniformly computable. We say has a (d-)decidable copy if there exists a model ≅ such that the elementary diagram of is (d-)computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous model with a 0-basis but no decidable copy. We extend this result here. Let d ≤ 0' be any low₂ degree. We show that there exists a (...)
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  9.  16
    The Degree Spectra of Homogeneous Models.Karen Lange - 2008 - Journal of Symbolic Logic 73 (3):1009-1028.
    Much previous study has been done on the degree spectra of prime models of a complete atomic decidable theory. Here we study the analogous questions for homogeneous models. We say a countable model A has a d-basis if the types realized in A are all computable and the Turing degree d can list $\Delta _{0}^{0}$ -indices for all types realized in A. We say A has a d-decidable copy if there exists a model B ≅ A such that the elementary (...)
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  10.  5
    A Decidable Ehrenfeucht Theory with Exactly Two Hyperarithmetic Models.Robert C. Reed - 1991 - Annals of Pure and Applied Logic 53 (2):135-168.
    Millar showed that for each n<ω, there is a complete decidable theory having precisely eighteen nonisomorphic countable models where some of these are decidable exactly in the hyperarithmetic set H. By combining ideas from Millar's proof with a technique of Peretyat'kin, the author reduces the number of countable models to five. By a theorem of Millar, this is the smallest number of countable models a decidable theory can have if some of the models are not 0″-decidable.
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