Timeline for Is Monsky's theorem dependent on the axiom of choice?
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Sep 13, 2012 at 1:29 | comment | added | Igor Rivin | Thanks! This is pretty much as the OP had conjectured, but I guess my point was that we were skating pretty close to the AC... | |
Sep 13, 2012 at 0:18 | comment | added | Andreas Blass | The use of the axiom of choice in the Hales-Strauss paper is needed to get non-Archimedean valuations on the whole real field. But in the proof of Monsky's theorem, they use the valuation only for the coordinates of the points involved in an alleged counterexample to Monsky's theorem. So, any particular alleged counterexample can be refuted by a non-Archimedean valuation on a much smaller field, in fact a countable subfield of the reals. And the existence of such valuations doesn't need choice. | |
Sep 12, 2012 at 21:21 | history | answered | Igor Rivin | CC BY-SA 3.0 |