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Jul 29, 2011 at 17:14 comment added Ravi Vakil "The existence of a Grothendieck universe is equivalent to the existence of an inaccessible cardinal." This sounds something you might read in a <a href="amazon.com/Angels-Demons-ebook/dp/B000FBJFSM/… Brown book</a>, about nefarious plots high up in the Catholic Church... :-)
Nov 3, 2010 at 21:18 comment added Andrés E. Caicedo Let me elaborate: Typically these inductions appear when there is some sort of ''topological derivative'' in the background, although there are of courses other settings. For a pretty example, look at the paper "Fixed Points, Koebe Uniformization and Circle Packings" by Zheng-Xu He and Oded Schramm, The Annals of Mathematics, Second Series, Vol. 137, No. 2, (Mar., 1993), pp. 369-406.
Nov 3, 2010 at 20:55 comment added Andrés E. Caicedo Inductions of length $\omega_1$ are not that uncommon in complex analysis, actually.
Nov 3, 2010 at 20:38 history answered Stefan Geschke CC BY-SA 2.5