= Solution
First express inaccessibility by universally excluding witnesses to its failure. Besides $\kappa$ being an ordinal greater than $\omega$, require that for every $\alpha<\kappa$ there is no function from $\alpha$ cofinal in $\kappa$, and no injection from $\kappa$ into $\mathcal P(\alpha)$. The first condition gives regular cardinalhood; the second says that $\kappa$ is a <strong limit cardinal>. Under the <axiom of choice> these are exactly the conditions for a <strongly inaccessible cardinal>.
These are <Pi-one formulas modulo ZF>: the only unbounded quantifiers universally range over possible functions. Being a function of the specified domain, having bounded or cofinal range in $\kappa$, and being an injection whose values are subsets of $\alpha$ can all be written with <bounded formulas in set theory>, without using a power-set object as an unbounded existential witness. Consequently inaccessibility is downward absolute to a transitive <inner model> of <ZFC>.
Now suppose $\kappa$ is Mahlo in $V$. It is inaccessible in the <constructible universe> $L$, and every $V$-inaccessible ordinal below it is also inaccessible in $L$. Let $C\in L$ be any set that $L$ regards as a <club set> in $\kappa$. Closure and unboundedness are absolute properties of this fixed set of ordinals, so $C$ is also a <club set> in $V$. By Mahloness in $V$, it contains an ordinal that is inaccessible in $V$, hence in $L$. Every $L$-club therefore meets the $L$-inaccessible ordinals below $\kappa$. Thus \b[<Mahloness is downward absolute to the constructible universe>]:
$$
\boxed{L\models\text{“}\kappa\text{ is Mahlo”}.}
$$
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