Logical and ontological aspects of a generalized arithmetic

• Grant number: 08/06205-5
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2009
• End date: February 28, 2011
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Walter Alexandre Carnielli
• Grantee: Anderson Beraldo de Araújo
• Host 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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

ARAÚJO, Anderson Beraldo de. A model-theoretical approach to classical Turing computability. 2011. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas Campinas, SP.