Completeness theorem for Dummett's LC quantified and some of its extensions (Q1207344)

Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame \(\langle Q^ +,\leq,D\rangle\), where \(Q^ +\) is the set of non-negative rational numbers, \(\leq\) is the numerical relation ``less or equal than'' and \(D\) is the domain function such that for all \(v,w\in Q^ +\), \(D_ w\neq\emptyset\), and if \(v\leq w\), then \(D_ v\subseteq D_ w\). Moreover, simple completeness proofs of extensions of Q-LC are given.