  Let $X$ be a complex topological vector space and $L(X)$ the set of all
continuous linear operators on $X.$ In this paper, we extend the notion of the
codiskcyclicity of a single operator $T\in L(X)$ to a set of operators
$\Gamma\subset L(X).$ We prove some results for codiskcyclic sets of operators
and we establish a codiskcyclicity criterion. As an application, we study the
codiskcyclicity of $C_0$-semigroups of operators.
