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Logical and ontological aspects of a generalized arithmetic

Grant number: 08/06205-5
Support type:Scholarships in Brazil - Doctorate (Direct)
Effective date (Start): March 01, 2009
Effective date (End): February 28, 2011
Field of knowledge:Humanities - Philosophy - Logic
Principal Investigator:Walter Alexandre Carnielli
Grantee:Anderson Beraldo de Araújo
Home Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

A generalized arithmetic is an extension of classical first-order Peano arithmetic generated by adding generalizations of the classical quantifiers, called modulated quantifiers. The general aim of this research is to study the potentialities of a generalized arithmetic for understanding the incompleteness results, obtained through semantical resources. Specifically, the research aims: 1) to examine the existence of nonstandard models of the extensions of classical first-order Peano arithmetic through modulated quantifiers; 2) to determine the validity of the first incompleteness theorem in a generalized arithmetic, specially with respect to S. Kripke's semantical proofs of that theorem; 3) to analyse J. Hintikka's approach of the incompleteness phenomenon, which uses branching quantifiers, in contrast to the generalized arithmetic to be developed. (AU)