15 found
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  1. Solving Pell Equations Locally in Models of IΔ0.Paola D'Aquino - 1998 - Journal of Symbolic Logic 63 (2):402-410.
    In [4] it is shown that only using exponentiation can one prove the existence of non trivial solutions of Pell equations in IΔ 0 . However, in this paper we will prove that any Pell equation has a non trivial solution modulo m for every m in IΔ 0.
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  2.  3
    Pell Equations and Exponentiation in Fragments of Arithmetic.Paola D'Aquino - 1996 - Annals of Pure and Applied Logic 77 (1):1-34.
    We study the relative strength of the two axioms Every Pell equation has a nontrivial solution Exponentiation is total over weak fragments, and we show they are equivalent over IE1. We then define the graph of the exponential function using only existentially bounded quantifiers in the language of arithmetic expanded with the symbol #, where # = x[log2y]. We prove the recursion laws of exponentiation in the corresponding fragment.
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  3.  12
    Local Behaviour of the Chebyshev Theorem in Models of Iδ.Paola D'Aquino - 1992 - Journal of Symbolic Logic 57 (1):12 - 27.
  4.  13
    Toward the Limits of the Tennenbaum Phenomenon.Paola D'Aquino - 1997 - Notre Dame Journal of Formal Logic 38 (1):81-92.
    We consider the theory and its weak fragments in the language of arithmetic expanded with the functional symbol . We prove that and its weak fragments, down to and , are subject to the Tennenbaum phenomenon with respect to , , and . For the last two theories it is still unknown if they may have nonstandard recursive models in the usual language of arithmetic.
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  5.  15
    < I> Δ< Sub> 0-Complexity of the Relation< I> Y_=< I> Π_< Sub> I⩽ N< I> F_(< I> I).Alessandro Berarducci & Paola D'Aquino - 1995 - Annals of Pure and Applied Logic 75 (1):49-56.
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  6.  8
    Δ0-Complexity of the Relation y = Πi ⩽ nF.Alessandro Berarducci & Paola D'Aquino - 1995 - Annals of Pure and Applied Logic 75 (1-2):49-56.
    We prove that if G is a Δ 0 -definable function on the natural numbers and F = Π i = 0 n G , then F is also Δ 0 -definable. Moreover, the inductive properties of F can be proved inside the theory IΔ 0.
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  7.  10
    A Sharpened Version of McAloon's Theorem on Initial Segments of Models of IΔ0.Paola D'Aquino - 1993 - Annals of Pure and Applied Logic 61 (1-2):49-62.
    A generalization is given of McAloon's result on initial segments ofmodels of GlΔ0, the fragment of Peano Arithmetic where the induction scheme is restricted to formulas with bounded quantifiers.
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  8.  9
    A Sharpened Version of McAloon's Theorem on Initial Segments of Models of< I> IΔ_< Sub> 0.Paola D'Aquino - 1993 - Annals of Pure and Applied Logic 61 (1):49-62.
    A generalization is given of McAloon's result on initial segments ofmodels of GlΔ0, the fragment of Peano Arithmetic where the induction scheme is restricted to formulas with bounded quantifiers.
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  9.  14
    Topological Duality for Diagonalizable Algebras.Claudio Bernardi & Paola D'Aquino - 1988 - Notre Dame Journal of Formal Logic 29 (3):345-364.
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  10.  15
    Preface.Uri Abraham, Lev Beklemishev, Paola D'Aquino & Marcus Tressl - 2016 - Annals of Pure and Applied Logic 167 (10):865-867.
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  11.  10
    Quotient Fields of a Model of IΔ0 + Ω1.Paola D'Aquino - 2001 - Mathematical Logic Quarterly 47 (3):305-314.
    In [4] the authors studied the residue field of a model M of IΔ0 + Ω1 for the principal ideal generated by a prime p. One of the main results is that M/ has a unique extension of each finite degree. In this paper we are interested in understanding the structure of any quotient field of M, i.e. we will study the quotient M/I for I a maximal ideal of M. We prove that any quotient field of M satisfies the (...)
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  12.  10
    A Note on the Decidability of Exponential Terms.Paola D'Aquino & Giuseppina Terzo - 2007 - Mathematical Logic Quarterly 53 (3):306-310.
    In this paper we prove, modulo Schanuel's Conjecture, that there are algorithms which decide if two exponential polynomials in π are equal in ℝ and if two exponential polynomials in π and i coincide in ℂ.
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  13.  7
    2012 European Summer Meeting of the Association for Symbolic Logic Logic Colloquium '12: Manchester, Uk July 12–18, 2012. [REVIEW]Paola D'Aquino - 2014 - Bulletin of Symbolic Logic 20 (3):369-410,.
  14.  5
    Solving Pell Equations Locally in Models of I$Delta_0$.Paola D'Aquino - 1998 - Journal of Symbolic Logic 63 (2):402-410.
    In [4] it is shown that only using exponentiation can one prove the existence of non trivial solutions of Pell equations in I$\Delta_0$. However, in this paper we will prove that any Pell equation has a non trivial solution modulo m for every m in I$\Delta_0$.
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  15.  17
    Local Behaviour of the Chebyshev Theorem in Models of $I\Delta_0$.Paola D'Aquino - 1992 - Journal of Symbolic Logic 57 (1):12-27.