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Model theory inspired in modern algebraic geometry

Grant number: 21/06193-1
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): August 01, 2021
Effective date (End): July 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal researcher:Hugo Luiz Mariano
Grantee:Gabriel Bittencourt Rios
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this work, we will study Model Theory from a algebro-geometric approach, that is to say, we will search the literature for the historical use of techniques analogous to schemes in the context of Categorial Model Theory. Centrally, the project will cover Steve Breiner's Ph.D thesis and related articles. Aiming at this, we firstly intend to insert the student in the context of Categorical Logic, with an emphasis on the use of Topoi for the study of Model Theory. Finally, we plan to take Breiner's ideas further: just as sheaves on a topological sapce were generalized to sheaves on a Grothendieck topology, we will try to bring the concept of logical schemes into a more general context. (AU)

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