In the book of Marcel Berger, Geometry 1, the Fundamental theorem of affine geometry is stated as:
Let $X,X'$ be affine spaces of same dimension $d\geq2$. Let $f:X \rightarrow X'$ be a bijection which takes any three collinear points $a,b,c\in X$ into collinear points $f(a),f(b),f(c) \in X'$. Then $f$ is semiaffine.
But this theorem doesn't make sense if the field is $F_2$. Because then any line which passes through let's say $a$ and $b$, is given by $a+k(b-a)$ where $k\in F_2$. And then this line contains only two points $a,b$, therefore makes no sense to speak of three distinct collinear points in this space. The theorem then would imply that any bijection is semiaffine, which is clearly false.
What is the Fundamental theorem of affine geometry in case the field has characteristic 2?