[FOM] 336:Undecidability/Euclidean geometry/2
Timothy Y. Chow
tchow at alum.mit.edu
Fri May 1 22:17:03 EDT 2009
Jan Pax wrote:
>Harvey Friedman wrote:
>>
>> An integral line system is a finite set of rational lines whose
>> intersection points have integer coordinates.
>>
>> We say that f is an equivalence between integral line systems S,T if
>> and only if f is a bijection from S onto T such that for any
>> L_1,...,L_k in S,
>
>I think, that here is missing some continuity condition on f, as is in
>the original formulation.
>
>What happens with theorems 1 and 2 if we require moreover that the
>bijection from S onto T maps every line of S _analytically_ onto a
>line of T?
I think you're misreading the theorems. In fact I'm not sure *how* you're
reading them, but perhaps you are thinking that f is a map from the
*plane* to itself that *carries* S to T, as opposed to a bijective
correspondence between the finite sets S and T? That's not what was being
asserted.
Tim
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