  $^{20}$Ne can be considered as a double-magic $^{16}$O core nucleus
surrounded by four nucleons, the constituents of an $\alpha$-like quartet.
Similar to other nuclei ($^{212}$Po, $^{104}$Ti, etc.) with a quartet on top of
a double-magic core nucleus, significant $\alpha$-like correlations are
expected. Correlations in the ground state of $^{20}$Ne are investigated using
different approaches. The quartetting wave function approach (QWFA) predicts a
large $\alpha$-like cluster contribution near the surface of the nuclei. The
Tohsaki-Horiuchi-Schuck-R\"opke (THSR) approach describes $\alpha$-like
clustering in nuclear systems. The results of the QWFA in the Thomas-Fermi and
shell-model approximation are compared with THSR calculations for the container
model. Results for the $\alpha$ formation probability and the rms radii are
shown.
