[FOM] 336:Undecidability/Euclidean geometry/2

[Timothy Y. Chow]

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