•  24
    Maximum Schemes in Arithmetic
    Mathematical Logic Quarterly 40 (3): 425-430. 1994.
    In this paper we deal with some new axiom schemes for Peano's Arithmetic that can substitute the classical induction, least-element, collection and strong collection schemes in the description of PA
  •  16
    On axiom schemes for T-provably $${\Delta_{1}}$$ Δ 1 formulas
    Archive for Mathematical Logic 53 (3-4): 327-349. 2014.
    This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are Δ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta_1}$$\end{document} provably in an arithmetic theory T. In particular, we determine the pr…Read more
  •  28
    We characterize the sets of all Π2 and all equation image theorems of IΠ−1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that IΠ−n + 1 is conservative over IΣ−n with respect to equation image sentences cannot be extended to Πn + 2 sentences. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, We…Read more
  • Herve pasqua, maître Eckhart. Le procès de l'un (review)
    Acta Philosophica 16 (2). 2007.
  •  1
    Los agustinos de La Habana colonial ante el liberalismo español
    Revista Agustiniana 49 (150): 885-913. 2008.
  •  15
    Induction, minimization and collection for Δ n+1 (T)–formulas
    Archive for Mathematical Logic 43 (4): 505-541. 2004.
    For a theory T, we study relationships among IΔ n +1 (T), LΔ n+1 (T) and B * Δ n+1 (T). These theories are obtained restricting the schemes of induction, minimization and (a version of) collection to Δ n+1 (T) formulas. We obtain conditions on T (T is an extension of B * Δ n+1 (T) or Δ n+1 (T) is closed (in T) under bounded quantification) under which IΔ n+1 (T) and LΔ n+1 (T) are equivalent. These conditions depend on Th Πn +2 (T), the Π n+2 –consequences of T. The first condition is connected …Read more
  •  17
    On the quantifier complexity of Δ n+1 (T)– induction
    Archive for Mathematical Logic 43 (3): 371-398. 2004.
    In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that IΔ n+1 (T) is Π n+2 –axiomatizable. In particular, IΔ n+1 (IΔ n+1 ) gives an axiomatization of Th Π n+2 (IΔ n+1 ) and is not finitely axiomatizable. This fact relates the fragment IΔ n+1 (IΔ n+1 ) to induction rule for Δ n+1 –formulas. Our arguments, invo…Read more