  We investigate different set-theoretic constructions in Residuated Logic
based on Fitting's work on Intuitionistic Set Theory. We start by stating some
results concerning constructible sets within valued models of Set Theory. We
present two distinct constructions of the constructible universe:
$\mathfrak{L}^{\mathbb{Q}}$ and $\mathbb{L}^{\mathbb{Q}}$, and show that they
are isomorphic to V (the classical von Neumann universe) and L (the classical
G\"odel constructible universe), respectively. Even though lattice-valued
models are the natural way to study non-classical Set Theory (e.g.,
Intuitionistic, Residuated, Paraconsistent Set Theory),our results prove that
the use of lattice-valued models is not suitable to study the notion of
constructibility in logics weaker than classical logic.
