Existence axioms in subtheories of ZFC and related axiomatic systems

• Grant number: 13/01011-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2013
• End date: April 30, 2017
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Itala Maria Loffredo D'Ottaviano
• Grantee: Edgar Luis Bezerra de Almeida
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In a series of three articles Freire develops an original analysis of the existence of sets in axiomatic system ZFC and some of its extensions; subtheories of ZFC are not considered in this work. However, there are some many foundational axiomatic systems of interest that are either subtheories of ZFC, or are extensions of subtheories of ZFC inconsistent with ZFC. We have, for example, (a) ZF subtheories with various weak principles of choice (b) subtheory obtained from ZFC by subtracting the axiom of infinity, and related systems for arithmetic, (c) theory Kripke-Platek, KP, which does not contain the full version of the axiom of understanding, (d) the system obtained from ZF by adding the axiom of determination (AD), among others. This research project aims to extend these analyzes to subtheories of ZFC and related systems, and appears thus as a research project in the area of axiomatic set theory and its classical fragments. (AU)

Academic Publications

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

ALMEIDA, Edgar Luis Bezerra de. Analysis of truth conditions and existential requirements in axiomatizations of arithmetic. 2017. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas Campinas, SP.