The large structures of Grothendieck founded on finite order arithmetic
C. McLarty. (2011)cite http://arxiv.org/abs/1102.1773arxiv:1102.1773Comment: Adds the optimality observation: this is the weakest possible foundation for these tools. The exposition is clarified, the set theory better motivated, and some proofs made fuller.
Such large-structure tools of cohomology as toposes and derived categories
stay close to arithmetic in practice, yet existing foundations for them go
beyond the strong set theory ZFC. We formalize the practical insight by
founding the theorems of EGA and SGA, plus derived categories, at the level of
finite order arithmetic. This is the weakest possible foundation for these
tools since one elementary topos of sets with infinity is already this strong.
[1102.1773] The large structures of Grothendieck founded on finite order arithmetic