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Willie Wong
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One of my papers did this for the existence of the maximal globally hyperbolic Cauchy development for the initial value problem in general relativity.

The TL;DR is that the original proof had a gratuitous use of Zorn's lemma. The fix is similar, but also somewhat different from, the fix removing the use of Zorn from maximal atlases.

Willie Wong
  • 39k
  • 4
  • 94
  • 176