Results for 'iterated power series fields'

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  1.  5
    Κ -Bounded Exponential-Logarithmic Power Series Fields.Salma Kuhlmann & Saharon Shelah - 2005 - Annals of Pure and Applied Logic 136 (3):284-296.
    In [F.-V. Kuhlmann, S. Kuhlmann, S. Shelah, Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 3177–3183] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows us to (...)
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  2.  31
    Elementary Properties of Power Series Fields Over Finite Fields.Franz-Viktor Kuhlmann - 2001 - Journal of Symbolic Logic 66 (2):771-791.
    In spite of the analogies between Q p and F p ((t)) which became evident through the work of Ax and Kochen, an adaptation of the complete recursive axiom system given by them for Q p to the case of F p ((t)) does not render a complete axiom system. We show the independence of elementary properties which express the action of additive polynomials as maps on F p ((t)). We formulate an elementary property expressing this action and show that (...)
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  3. Undecidable Wreath Products and Skew Power Series Fields.Françoise Delon & Patrick Simonetta - 1998 - Journal of Symbolic Logic 63 (1):237-246.
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  4.  4
    Ax James. On the Undecidability of Power Series Fields. Proceedings of the American Mathematical Society, Vol. 16 , P. 846. [REVIEW]Abraham Robinson - 1971 - Journal of Symbolic Logic 36 (4):684-684.
  5.  3
    Review: James Ax, On the Undecidability of Power Series Fields[REVIEW]Abraham Robinson - 1971 - Journal of Symbolic Logic 36 (4):684-684.
  6.  8
    Periodicite Des Theories Elementaires Des Corps De Series Formelles Iterees.Françoise Delon - 1986 - Journal of Symbolic Logic 51 (2):334-351.
    C. U. Jensen suggested the following construction, starting from a field $K: K_0 = K, K_{\alpha + 1} = K_\alpha ((X_\alpha)), K_\alpha = \bigcup K_\beta$ if $\alpha$ is limit and asked when two fields $k_\alpha$ and $K_\beta$ are equivalent. We give a complete answer in the case of a field $K$ of characteristic 0.
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  7.  7
    Analytic Functions Over a Field of Power Series.Marie-Hélène Mourgues - 2002 - Archive for Mathematical Logic 41 (7):631-642.
    We extend the notion of absolute convergence for real series in several variables to a notion of convergence for series in a power series field ℝ((t Γ)) with coefficients in ℝ. Subsequently, we define a natural notion of analytic function at a point of ℝ((t Γ))m. Then, given a real function f analytic on a open box I of ℝ m , we extend f to a function f ★ which is analytic on a subset of (...)
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  8.  28
    Joseph Becker and Leonard Lipshitz. Remarks on the Elementary Theories of Formal and Convergent Power Series. Fundament a Mathematicae, Vol. 105 , Pp. 229–239. - Françoise Delon. Indécidabilité de la Théorie des Anneaux de Séries Formelles À Plusiers Indéterminées. Fundament a Mathematicae, Vol. 112 , Pp. 215–229. - J. Becker, J. Denef, and L. Lipshitz. Further Remarks on the Elementary Theory of Formal Power Series Rings. Model Theory of Algebra and Arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic Held at Karpacz, Poland, September 1–7, 1979, Edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture Notes in Mathematics, Vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, Pp. 1–9. - Françoise Delon. Hensel Fields in Equal Characteristic P > 0. Model Theory of Algebra and Arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic Held at Karpacz, Poland, September 1–7, 1979, Edited By. [REVIEW]S. Basarab - 1985 - Journal of Symbolic Logic 50 (3):853-854.
  9.  16
    Lou van den Dries, Angus Macintyre, and David Marker. The Elementary Theory of Restricted Analytic Fields with Exponentiation. Annals of Mathematics, Ser. 2 Vol. 140 , Pp. 183–205. - Lou van den Dries, Angus Macintyre, and David Marker. Logarithmic-Exponential Power Series. Journal of the London Mathematical Society, Ser. 2 Vol. 56 , Pp. 417–434. [REVIEW]Chris Miller - 2000 - Bulletin of Symbolic Logic 6 (2):213-216.
  10.  8
    Review: Lou van den Dries, Angus Macintyre, David Marker, The Elementary Theory of Restricted Analytic Fields with Exponentiation; Lou van den Dries, Angus Macintyre, David Marker, Logarithmic-Exponential Power Series[REVIEW]Chris Miller - 2000 - Bulletin of Symbolic Logic 6 (2):213-216.
  11.  9
    Algebraic Properties of Rings of Generalized Power Series.Daniel Pitteloud - 2002 - Annals of Pure and Applied Logic 116 (1-3):39-66.
    The fields K) of generalized power series with coefficients in a field K and exponents in an additive abelian ordered group G play an important role in the study of real closed fields. The subrings K) consisting of series with non-positive exponents find applications in the study of models of weak axioms for arithmetic. Berarducci showed that the ideal JK) generated by the monomials with negative exponents is prime when is the additive group of the (...)
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  12.  16
    Existence of Prime Elements in Rings of Generalized Power Series.Daniel Pitteloud - 2001 - Journal of Symbolic Logic 66 (3):1206-1216.
    The field K((G)) of generalized power series with coefficients in the field K of characteristic 0 and exponents in the ordered additive abelian group G plays an important role in the study of real closed fields. Conway and Gonshor (see [2, 4]) considered the problem of existence of non-standard irreducible (respectively prime) elements in the huge "ring" of omnific integers, which is indeed equivalent to the existence of irreducible (respectively prime) elements in the ring K((G ≤ 0 (...)
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  13.  25
    The Field of LE-Series with a Nonstandard Analytic Structure.Ali Bleybel - 2011 - Notre Dame Journal of Formal Logic 52 (3):255-265.
    In this paper we prove that the field of Logarithmic-Exponential power series endowed with the exponential function and a class of analytic functions containing both the overconvergent functions in the t -adic norm and the usual strictly convergent power series is o-minimal.
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  14.  18
    Comparison of Exponential-Logarithmic and Logarithmic-Exponential Series.Salma Kuhlmann & Marcus Tressl - 2012 - Mathematical Logic Quarterly 58 (6):434-448.
    We explain how the field of logarithmic-exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential-logarithmic series constructed in 9, 6, and 13. On the other hand, we explain why no field of exponential-logarithmic series embeds in the field of logarithmic-exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non-isomorphic models of Thequation image; the elementary theory of the ordered field of (...)
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  15.  29
    Contentious Politics: Hobbes, Machiavelli and Corporate Power.Sandra Leonie Field - 2015 - Democracy Futures Series, The Conversation.
    Political protesters often don’t play by the rules. Think of the Occupy Movement, which brought lower Manhattan to a standstill in 2011 under the slogan, “We are the 99%”. Closer to home, think of the refugee activists who assisted a breakout from South Australia’s Woomera detention centre in 2002. Both are examples of contentious politics, or forms of political engagement outside the institutional channels of political decision-making. The democratic credentials of contentious politics are highly ambivalent. On the one hand, contentious (...)
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  16.  13
    On the Structure of Nonarchimedean Exponential Fields I.Salma Kuhlmann - 1995 - Archive for Mathematical Logic 34 (3):145-182.
    Given an ordered fieldK, we compute the natural valuation and skeleton of the ordered multiplicative group (K >0, ·, 1, <) in terms of those of the ordered additive group (K,+,0,<). We use this computation to provide necessary and sufficient conditions on the value groupv(K) and residue field $\bar K$ , for theL ∞ε-equivalence of the above mentioned groups. We then apply the results to exponential fields, and describev(K) in that case. Finally, ifK is countable or a power (...)
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  17.  1
    Sigma-Prikry Forcing II: Iteration Scheme.Alejandro Poveda, Assaf Rinot & Dima Sinapova - forthcoming - Journal of Mathematical Logic:2150019.
    In Part I of this series [5], we introduced a class of notions of forcing which we call [Formula: see text]-Prikry, and showed that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality are [Formula: see text]-Prikry. We proved that given a [Formula: see text]-Prikry poset [Formula: see text] and a [Formula: see text]-name for a nonreflecting stationary set [Formula: see text], there exists a corresponding [Formula: see text]-Prikry poset that projects to (...)
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  18.  17
    On the Elimination of Imaginaries From Certain Valued Fields.Philip Scowcroft & Angus Macintyre - 1993 - Annals of Pure and Applied Logic 61 (3):241-276.
    A nontrivial ring with unit eliminates imaginaries just in case its complete theory has the following property: every definable m-ary equivalence relation E may be defined by a formula f = f, where f is an m-ary definable function. We show that for certain natural expansions of the field of p-adic numbers, elimination of imaginaries fails or is independent of ZPC. Similar results hold for certain fields of formal power series.
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  19. School Trouble: Identity, Power and Politics in Education.Deborah Youdell - 2010 - Routledge.
    What is the trouble with schools and why should we want to make ‘school trouble’? Schooling is implicated in the making of educational and social exclusions and inequalities as well as the making of particular sorts of students and teachers. For this reason schools are important sites of counter- or radical- politics. In this book, Deborah Youdell brings together theories of counter-politics and radical traditions in education to make sense of the politics of daily life inside schools and explores a (...)
     
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  20.  2
    Neural Network-Based Intelligent Computing Algorithms for Discrete-Time Optimal Control with the Application to a Cyberphysical Power System.Feng Jiang, Kai Zhang, Jinjing Hu & Shunjiang Wang - 2021 - Complexity 2021:1-10.
    Adaptive dynamic programming, which belongs to the field of computational intelligence, is a powerful tool to address optimal control problems. To overcome the bottleneck of solving Hamilton–Jacobi–Bellman equations, several state-of-the-art ADP approaches are reviewed in this paper. First, two model-based offline iterative ADP methods including policy iteration and value iteration are given, and their respective advantages and shortcomings are discussed in detail. Second, the multistep heuristic dynamic programming method is introduced, which avoids the requirement of initial admissible control and achieves (...)
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  21.  22
    Normal Functors, Power Series and Lambda-Calculus.Jean-Yves Girard - 1988 - Annals of Pure and Applied Logic 37 (2):129.
  22. Um Episódio do debate contempor'neo ao redor da antropologia filosófica: Série 2 / A Contemporaneous Debate Episode About the Philosophical Anthropology.Roberto Nigro - 2011 - Kant E-Prints 6:14-31.
    In the beginning of the 20 th century, the discussion of the anthropological theme across the field of French philosophical debate. It also implies a redefinition of philosophy and politics at different levels. This is about the second episode of great anthropological questioning that took place in the 20th century, since the first had to do with the great German philosophical works which draws on the writings of Max Scheler, Martin Heidegger, Helmuth Plessner, Arnold Gehlen, and Ernst Cassirer, among others. (...)
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  23.  4
    A Method for Accelerating of Convergence of Numerical and Power Series.Murat Sadiku - 2019 - Seeu Review 14 (2):114-121.
    In this paper is examined the acceleration of convergence of alternative and non-alternative numerical and power series by means of an Euler-Abel type operator, that is defined earlier by G.A.Sorokin and I.Z.Milovanovic. Through this type of linear operator of generalized difference of sequence is achieved that alternative and non-alternative numerical and power series to be transformed into series with higher speed of convergence than the initial series. At the end of this paper is given (...)
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  24.  20
    Analytical Solution for the Time Fractional BBM-Burger Equation by Using Modified Residual Power Series Method.Jianke Zhang, Zhirou Wei, Longquan Yong & Yuelei Xiao - 2018 - Complexity 2018:1-11.
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  25.  8
    Authors Meets Readers: Martin Powers in Conversation with Sandra Field, Jeffrey Flynn, Stephen Macedo, and Longxi Zhang. [REVIEW]Sandra Leonie Field, Jeffrey Flynn, Stephen Macedo, Longxi Zhang & Martin Powers - 2020 - Journal of World Philosophies 5 (1):188-240.
    Sandra Field, Jeffrey Flynn, Stephen Macedo, Longxi Zhang, and Martin Powers discussed Powers’ book China and England: The Preindustrial Struggle for Social Justice in Word and Image at the American Philosophical Association’s 2020 Eastern Division meeting in Philadelphia. The panel was sponsored by the APA’s “Committee on Asian and Asian-American Philosophers and Philosophies” and organized by Brian Bruya.
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  26.  5
    Least-Squares Residual Power Series Method for the Time-Fractional Differential Equations.Jianke Zhang, Zhirou Wei, Lifeng Li & Chang Zhou - 2019 - Complexity 2019:1-15.
    In this study, an applicable and effective method, which is based on a least-squares residual power series method, is proposed to solve the time-fractional differential equations. The least-squares residual power series method combines the residual power series method with the least-squares method. These calculations depend on the sense of Caputo. Firstly, using the classic residual power series method, the analytical solution can be solved. Secondly, the concept of fractional Wronskian is introduced, which (...)
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  27.  3
    Analytical Solution of the Fractional Fredholm Integrodifferential Equation Using the Fractional Residual Power Series Method.Muhammed I. Syam - 2017 - Complexity 2017:1-6.
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  28.  12
    A Note on Ordinal Numbers and Rings of Formal Power Series.Kostas Hatzikiriakou - 1994 - Archive for Mathematical Logic 33 (4):261-263.
  29.  23
    Un Principe d'Ax-Kochen-Ershov Pour Des Structures Intermediares Entre Groupes Et Corps Values.Françoise Delon & Patrick Simonetta - 1999 - Journal of Symbolic Logic 64 (3):991-1027.
    An Ax-Kochen-Ershov principle for intermediate structures between valued groups and valued fields. We will consider structures that we call valued B-groups and which are of the form $\langle G, B, *, v\rangle$ where - G is an abelian group, - B is an ordered group, - v is a valuation defined on G taking its values in B, - * is an action of B on G satisfying: ∀ x ∈ G ∀ b ∈ B v(x * b) = (...)
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  30.  75
    Field Metaphysic, Power, and Individuation in Spinoza.Valtteri Viljanen - 2007 - Canadian Journal of Philosophy 37 (3):393-418.
    Spinoza developed a highly interesting metaphysical theory of nature and individuality. In this paper, I endeavor to bring forward some ideas on how Spinozistic views on extended substance, physical world, and individuality can be approached using the concept of power as the basis of interpretation. Jonathan Bennett's ‘field metaphysical’ interpretation of Spinoza's doctrine of one extended substance has generated much discussion, and forms the other starting point of my paper. I believe that the field metaphysical interpretation enables one to (...)
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  31.  83
    The Power of Naive Truth.Hartry Field - forthcoming - Review of Symbolic Logic:1-34.
    Nonclassical theories of truth that take truth to be transparent have some obvious advantages over any classical theory of truth. But several authors have recently argued that there’s also a big disadvantage of nonclassical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that the resulting internal theories are (...)
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  32.  19
    Comparative Expectations.Arthur Paul Pedersen - 2014 - Studia Logica 102 (4):811-848.
    I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archimedean condition on an agent’s comparative judgments, it does not require the (...)
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  33.  3
    Power Grid Fault Diagnosis Method Using Intuitionistic Fuzzy Petri Nets Based on Time Series Matching.Mingyue Tan, Jiming Li, Xiangqian Chen & Xuezhen Cheng - 2019 - Complexity 2019:1-14.
    To improve the reliability of power grid fault diagnosis by enhancing the processing ability of uncertain information and adequately utilizing the alarm information about power grids, a fault diagnosis method using intuitionistic fuzzy Petri Nets based on time series matching is proposed in this paper. First, the alarm hypothesis sequence and the real alarm sequence are constructed using the alarm information and the general grid protection configuration model, and the similarity of the two sequences is used to (...)
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  34.  8
    Pluralizing Field Analysis: Toward a Relational Understanding of the Field of Power.Andreas Schmitz, Daniel Witte & Vincent Gengnagel - 2017 - Social Science Information 56 (1):49-73.
    A crucial yet often-overlooked starting point for any Bourdieusian field analysis is to relate the field under consideration to the ‘field of power’, so as to enable an examination of its relative autonomy or heteronomy, i.e. its relation to other fields of society and to society as a whole. However, Bourdieu and his successors did not implement this key conceptual consideration systematically, or did so peripherally at best. For this reason both the theoretical and the empirical status of (...)
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  35. The Power of Naive Truth.Hartry Field - manuscript
    While non-classical theories of truth that take truth to be transparent have some obvious advantages over any classical theory that evidently must take it as non-transparent, several authors have recently argued that there's also a big disadvantage of non-classical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that (...)
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  36.  39
    In Vitro Eugenics.Robert Sparrow - 2014 - Journal of Medical Ethics 40 (11):725-731.
    A series of recent scientific results suggest that, in the not-too-distant future, it will be possible to create viable human gametes from human stem cells. This paper discusses the potential of this technology to make possible what I call ‘in vitro eugenics’: the deliberate breeding of human beings in vitro by fusing sperm and egg derived from different stem-cell lines to create an embryo and then deriving new gametes from stem cells derived from that embryo. Repeated iterations of this (...)
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  37. Potentia: Hobbes and Spinoza on Power and Popular Politics.Sandra Leonie Field - 2020 - New York, NY, USA: Oxford University Press.
    This book offers a detailed study of the political philosophies of Thomas Hobbes and Benedict de Spinoza, focussing on their concept of power as potentia, concrete power, rather than power as potestas, authorised power. The focus on power as potentia generates a new conception of popular power. Radical democrats–whether drawing on Hobbes's 'sleeping sovereign' or on Spinoza's 'multitude'–understand popular power as something that transcends ordinary institutional politics, as for instance popular plebsites or mass (...)
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  38. M. Gitik Blowing Up Power of a Singular cardinalYwider Gaps 1 D. Pitteloud Algebraic Properties of Rings of Generalized Power Series 39.I. Neeman, D. M. Evans, M. Menni, R. D. Schindler, K. Ho & F. Stephan - 2002 - Annals of Pure and Applied Logic 116 (1):3-15.
  39.  2
    Improving Power System Stability with Gramian Matrix-Based Optimal Setting of a Single Series FACTS Device: Feasibility Study in Vietnamese Power System.Doan le Van DaiDuc Tung, Tran Le Thang Dong & Le Cao Quyen - 2017 - Complexity 2017:1-21.
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  40. Hobbes and the Question of Power.Sandra Field - 2014 - Journal of the History of Philosophy 52 (1):61-85.
    Thomas Hobbes has been hailed as the philosopher of power par excellence; however, I demonstrate that Hobbes’s conceptualization of political power is not stable across his texts. Once the distinction is made between the authorized and the effective power of the sovereign, it is no longer sufficient simply to defend a doctrine of the authorized power of the sovereign; such a doctrine must be robustly complemented by an account of how the effective power commensurate to (...)
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  41.  5
    The Field of Reals with a Predicate for the Real Algebraic Numbers and a Predicate for the Integer Powers of Two.Mohsen Khani - 2015 - Archive for Mathematical Logic 54 (7-8):885-898.
    Given a theory T of a polynomially bounded o-minimal expansion R of R¯=⟨R,+,.,0,1,<⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{\mathbb{R}} = \langle\mathbb{R}, +,., 0, 1, < \rangle}$$\end{document} with field of exponents Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Q}}$$\end{document}, we introduce a theory T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{T}}$$\end{document} whose models are expansions of dense pairs of models of T by a discrete multiplicative group. We prove that T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...)
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  42.  27
    Expansions of the Real Field with Power Functions.Chris Miller - 1994 - Annals of Pure and Applied Logic 68 (1):79-94.
    We investigate expansions of the ordered field of real numbers equipped with a family of real power functions. We show in particular that the theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization. We derive that every function of one variable definable in this structure, not ultimately identically 0, is asymptotic at + ∞ to a real function of the (...)
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  43.  51
    From Ruling Class to Field of Power: An Interview with Pierre Bourdieu on La Noblesse d'État.Loïc J. D. Wacquant - 1993 - Theory, Culture and Society 10 (3):19-44.
  44.  24
    Raising to Powers in Algebraically Closed Fields.B. Zilber - 2003 - Journal of Mathematical Logic 3 (02):217-238.
    We study structures on the fields of characteristic zero obtained by introducing operations of raising to power. Using Hrushovski–Fraisse construction we single out among the structures exponentially-algebraically closed once and prove, under certain Diophantine conjecture, that the first order theory of such structures is model complete and every its completion is superstable.
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  45.  39
    Iterative and Fixed Point Common Belief.Aviad Heifetz - 1999 - Journal of Philosophical Logic 28 (1):61-79.
    We define infinitary extensions to classical epistemic logic systems, and add also a common belief modality, axiomatized in a finitary, fixed-point manner. In the infinitary K system, common belief turns to be provably equivalent to the conjunction of all the finite levels of mutual belief. In contrast, in the infinitary monotonic system, common belief implies every transfinite level of mutual belief but is never implied by it. We conclude that the fixed-point notion of common belief is more powerful than the (...)
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  46.  60
    Reapproaching Ramsey: Conditionals and Iterated Belief Change in the Spirit of AGM.Hans Rott - 2011 - Journal of Philosophical Logic 40 (2):155-191.
    According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse (...)
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  47.  71
    Political Power and Depoliticised Acquiescence: Spinoza and Aristocracy.Sandra Leonie Field - 2020 - Constellations 27 (4):670-684.
    According to a recent interpretive orthodoxy, Spinoza is a profoundly democratic theorist of state authority. I reject this orthodoxy. To be sure, for Spinoza, a political order succeeds in proportion as it harnesses the power of the people within it. However, Spinoza shows that political inclusion is only one possible strategy to this end; equally if not more useful is political exclusion, so long as it maintains what I call the depoliticised acquiescence of those excluded.
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  48. The State Nobility Elite Schools in the Field of Power.Pierre Bourdieu - 1996
  49.  1
    Field Theory, Media Change and the New Citizen Movements: Spain’s ‘Real Democracy’ Turn as a Series of Fields and Spaces.John Postill - 2017 - Recerca.Revista de Pensament I Anàlisi 21:15-36.
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  50.  3
    Interpreting Arithmetic in the First-Order Theory of Addition and Coprimality of Polynomial Rings.Javier Utreras - 2019 - Journal of Symbolic Logic 84 (3):1194-1214.
    We study the first-order theory of polynomial rings over a GCD domain and of the ring of formal entire functions over a non-Archimedean field in the language $\{ 1, +, \bot \}$. We show that these structures interpret the first-order theory of the semi-ring of natural numbers. Moreover, this interpretation depends only on the characteristic of the original ring, and thus we obtain uniform undecidability results for these polynomial and entire functions rings of a fixed characteristic. This work enhances results (...)
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