Because the resolution of an objective is limited by the diffraction of its circular aperture, I don't understand why an infinite lens can not have an infinitely good resolution power.
People use Abbe relation to compute the minimum resolvable distance $p_m$ of an objective as a function of its numerical aperture NA:
$p_m = \frac{1.22 \lambda}{NA} = \frac{1.22 \lambda}{n \sin(\theta_m)}$
When the aperture goes to infinity, $\sin \theta_m$ goes to 1 and thus the minimum resolvable distance is : $p_m = \frac{1.22 \lambda}{n}$
Now, the Airy disk created by the diffraction by a circular aperture of diameter $D$ has a radius defined by the zero of the $J_1$ Bessel function : $r_{Airy} = \frac{1.22 \lambda z}{D}$, where $z$ is the distance of the observation plane.
So the radius of the Airy disk goes to zero as the circular aperture goes to infinity. Why isn't it the case for the minimum resolvable distance when the lens diameter goes to infinity ?