The large structures of grothendieck founded on finite-order arithmetic

Review of Symbolic Logic 13 (2):296-325 (2020)

Authors
Colin McLarty
Case Western Reserve University
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.
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DOI 10.1017/s1755020319000340
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Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
The Strength of Mac Lane Set Theory.A. R. D. Mathias - 2001 - Annals of Pure and Applied Logic 110 (1-3):107-234.

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