  Highly accurate measurements of the $g$-factor of boronlike Ar are currently
implemented within the ARTEMIS experiment at GSI (Darmstadt, Germany) and
within the ALPHATRAP experiment at the MPIK (Heidelberg, Germany). A comparison
with the corresponding theoretical predictions will allow one to test the
modern methods of bound-state QED. However, at least three different
theoretical values of the \emph{g}-factor have been published up to date. The
systematic study of the \emph{g} factor value of Ar$^{13+}$ in the ground
$[(1s)^2(2s)^2 2p]^2P_{1/2}$ and the first excited $[(1s)^2(2s)^2 2p]^2P_{3/2}$
states is performed within the high order coupled cluster and configuration
interaction theories up to the full configuration interaction treatment.
Correlation contributions are discussed and results are compared with previous
studies.
