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THE LARGE STRUCTURES OF GROTHENDIECK FOUNDED ON FINITE-ORDER ARITHMETIC

Published online by Cambridge University Press:  02 August 2019

COLIN MCLARTY*
Affiliation:
Departments of Philosophy and Mathematics, Case Western Reserve University
*Corresponding
*DEPARTMENTS OF PHILOSOPHY AND MATHEMATICS CASE WESTERN RESERVE UNIVERSITY 10900 EUCLID AVENUE CLEVELAND, OH 44106, USA E-mail: colin.mclarty@case.edu

Abstract

The large-structure tools of cohomology including toposes and derived categories stay close to arithmetic in practice, yet published foundations for them go beyond ZFC in logical strength. We reduce the gap by founding all the theorems of Grothendieck’s SGA, plus derived categories, at the level of Finite-Order Arithmetic, far below ZFC. This is the weakest possible foundation for the large-structure tools because one elementary topos of sets with infinity is already this strong.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2019 

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References

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