10 citations · 14 across the 6 of their papers we have counts for
6 papers
On the depth of Wiles's proof of Fermat's Last Theorem
Yong Cheng, Colin McLarty
What constitutes depth in a mathematical proof? This paper addresses this foundational question through a close case study of Andrew Wiles's proof of Fermat's Last Theorem. We prop…
The finiteness theorem for invariants of a finite group (translation of Emmy Noether's "Der Endlichkeitsatz der Invarianten endlicher Gruppen")
Colin McLarty
A translation of Emmy Noether's paper "Der Endlichkeitsatz der Invarianten endlicher Gruppen" (Mathematische Annalen, vol. 77, 1920, pages 89--92). In Noether's words, the paper gi…
A univalent universe in finite order arithmetic
Colin McLarty
Homotopy Type Theory with a univalent universe is interpreted at the strength of finite order arithmetic. We eliminate Grothendieck universes, avoid the axiom of…
Zariski cohomology in second order arithmetic
Colin McLarty
The cohomology of coherent sheaves and sheaves of Abelian groups on Noetherian schemes are interpreted in second order arithmetic by means of a finiteness theorem. This finiteness…
Interpreting set theory in higher order arithmetic
Colin McLarty
A folk theorem says higher order arithmetic has the proof theoretic strength of set theory with limited power set. This paper makes the theorem precise in terms of several axiom sy…
The large structures of Grothendieck founded on finite order arithmetic
Colin McLarty
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 Z…