[FOM] 336:Undecidability/Euclidean geometry/2

[pax0@seznam.cz]

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?

Thank you, Jan Pax

>  L_1,...,L_k have a common point if and only if f(L_1),...,f(L_k) have  
>  a common point.
>