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Axiomatic systems for set theory

Grant number: 12/20599-1
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): March 01, 2013
Effective date (End): February 28, 2014
Field of knowledge:Humanities - Philosophy
Principal Investigator:Walter Alexandre Carnielli
Grantee:Rodrigo de Alvarenga Freire
Home 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


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.