A Finite Order Arithmetic Foundation for Cohomology

  title={A Finite Order Arithmetic Foundation for Cohomology},
  author={Colin McLarty},
Large-structure tools like toposes and derived categories in cohomology never go far from arithmetic in practice, yet existing formalizations are stronger than ZFC. We formalize the practical insight by grounding the entire toolkit of EGA and SGA at the level of finite order arithmetic. Grothendieck pre-empted many set theoretic issues in cohomology by positing a universe: “a set ‘large enough’ that the habitual operations of set theory do not go outside it” (SGA 1 VI.1 p. 146). His universes… CONTINUE READING


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Sheaves in Geometry and Logic

  • S. Mac Lane, I. Moerdijk
  • New York,
  • 1992
Highly Influential
4 Excerpts

A conservative extension of Peano Arithmetic

  • G. Cambridge University Press. Takeuti
  • Two Appli-
  • 1978
Highly Influential
3 Excerpts

The impact of Gödel’s incompleteness theorems on

  • A. Verlag. Macintyre
  • 2011
1 Excerpt

Concrete mathematical incompleteness

  • A. Grothendieck
  • 2010

Derived categories and Grothendieck duality

  • A. Neeman
  • 2010

Foundations of Grothendieck Duality

  • J. Lipman, M. Hashimoto
  • 2009
1 Excerpt

Moduli of finite flat group schemes, and modularity

  • M. Kisin
  • Annals of Mathematics
  • 2009
3 Excerpts

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