Aida Fernandez

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 with descriptions of Th Πn +2 (T) as IΣ n plus a class of nondecreasing total Π n –functions, and the second one is related with the equivalence between Δ n+1 (T)–formulas and bounded formulas (of a language extending the language of Arithmetic). This last property is closely tied to a general version of a well known theorem of R. Parikh. Using what we call Π n –envelopes we give uniform descriptions of the previous classes of nondecreasing total Π n –functions. Π n –envelopes are a generalization of envelopes (see [10]) and are closely related to indicators (see [12]). Finally, we study the hierarchy of theories IΔ n+1 (IΣ m ), m≥n, and prove a hierarchy theorem

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, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons’ conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for Π n+2 and Δ n+1 formulas (see [2])

Diabetes has been associated with affective disorders which complicate the management of the disease. Emotional intelligence, or the ability to perceive, facilitate, understand, and regulate emotions, has shown to be a protective factor of emotional disorders in general population. The main objective of this study was to systematically review the role of the EI construct in Type 1 and Type 2 diabetics and to observe how EI is related to biological and psychological variables. Comprehensive searches were conducted in PubMed, Scopus, PsycInfo, and Cochrane without time limitations, for studies examining the link between diabetes and EI. A total of 12 eligible studies were selected according to the inclusion criteria. We divided the results into four sections: EI and hemoglobin glycosylated, EI training effects, differences in EI between persons with diabetes and without diabetes, and EI and psychological adjustment and well-being. The results showed negative correlations between EI and HbA1c, positive effects of EI training on quality of life, anxiety, and glycemic control, no differences in EI between people with diabetes and healthy individuals, and, finally, negative correlations between EI and different psychological variables such as diabetes-related anxiety and distress, and positive correlations with quality of life, well-being, and marital satisfaction. This systematic review offers a starting point for a theoretical and practical understanding of the role played by EI in the management of diabetes and reveals that EI is a promising protective factor for biological and psychological variables in this population.

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, Weinheim.