Axiomatic Systems for Set Theory

• Grant number: 12/20599-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2013
• End date: February 28, 2014
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Walter Alexandre Carnielli
• Grantee: Rodrigo de Alvarenga Freire
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 10/51038-0 - Logical consequence, reasoning and computation - LOGCONS, AP.TEM

Abstract

The axiomatization of ZFC set theory intends to describe the universe of all sets. This universe has an intuitive description known as the "iterative, cumulative hierarchy of sets". According to this description, sets are "produced" in levels: in a given level, all sets produced in earlier levels, and only those, are available as elements for the production of new sets. Therefore, it seems that the systematic analysis of existence, and related notions, may be useful in order to compare different axiomatizations. The aim of the present project is twofold: to develop new tools to analyse and compare different axiomatizations, and to analyse the search for new axioms itself from the perspective of set existence.