  In the present article, we extend the fragment of inductive formulas for the
hybrid language L(@) in [8] including a McKinsey-like formula, and show that
every formula in the extended class has a first-order correspondent, by
modifying the algorithm hybrid-ALBA in [8]. We also identify a subclass of this
extended inductive fragment, namely the extended skeletal formulas, which
extend the class of skeletal formulas in [8], each formula in which axiomatize
a complete hybrid logic. Our proof method here is proof-theoretic, following
[10, 19] and [3, Chapter 14], in contrast to the algebraic proof in [8].
