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Is this question acceptable?: Is this a real question about Scott domains?

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    I entered a vote to close http://mathoverflow.net/questions/45780/from-domains-of-finitely-presented-groups-to-continuous-functors as not a real question, but I thought I'd ask here.
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    It sounded like "not a real question" to me too, but I was waiting to see if other people had that opinion
    before I voted to close.
    • CommentAuthorYemon Choi
    • CommentTimeNov 12th 2010
     

    I agree with Todd's remarks over there. One indicator, to me at least, is the use of the phrase "I want to start the thread with a thought".

    I think there might be an appropriate question lurking unformed in there, but it would do the original poster good to try and work out what he or she wants to ask.

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    Something approximating the question might be: is there a natural partial order on the set of finitely presented groups which is a Scott domain? His surrounding text looks like an attempt to motivate the question. There is also a suggestion of: is the subgroup order on finitely presented groups the partial order of a Scott domain?, but I'm afraid I don't quite understand the subgroup relation, since there may be many monomorphisms from one FPG to another (e.g., the free group on three generators is isomorphic to a subgroup of the free group on two generators in many ways). If it were me, I might look at the relation gotten by saying one finite presentation is less than another if the set of generators is the same and the relator subgroup of the first is contained in the second, something like that.

    But this is my whole point: finding out what he really means to ask precisely sounds a bit like a fishing expedition, hence not really suitable as an MO question. Yemon said much the same thing more succinctly.

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