On strange efficiency of ultraproducts in mathematics
Posted on November 6, 2017 by DimaIntriguing use of ultraproducts:
- Denef-Lipschitz proof of Artin approximation: one, two (follow ups by Schoutens);
- Robinson’s proof of Siegel theorem;
- Mustata’s limits of log-canonical thresholds;
- Arapura’s paper on Frobenius amplitudes ;
- Deligne’s categories \(S_t\);
- Kanel-Belov’s work on Dixmier conjecture;
- Olivier Fabert’s non-standard dimensional functional spaces and Gromov squeezing.
Somewhat understandable use of ultraproducts:
- sofic groups via metric ultraproducts;
- van den Dries-Wilkie’s construction of asymptotic cones;
- Goldbring’s local Hilbert 5th problem and Hrushovski’s Lie models.