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Timeline for Decidability of the generated order

Current License: CC BY-SA 3.0

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Oct 6, 2012 at 23:55 comment added Andreas Blass For real-closed fields, the decision procedure is primitive recursive, in fact "merely" double-exponential time (which I wouldn't call efficient). See for example en.wikipedia.org/wiki/Real_closed_field. Fields that are merely dense in their real-closures are likely to cause trouble. Even for the rationals, your question will involve arithmetical issues that I'd expect to be undecidable.
Oct 6, 2012 at 18:49 vote accept Lilach Leibovich
Oct 6, 2012 at 17:01 comment added Lilach Leibovich hmm, yes, I forgot to mention (actually, any field which is dense in its real closure). Are there known relativley efficient algorithmm to it (i.e is it atleast primitive recursive), maybe using SOS stuff?
Oct 6, 2012 at 16:48 history answered Andreas Blass CC BY-SA 3.0