The present paper has three objectives: Presenting an actualization of a proof of the decidability of monadic predicates logic in the contemporary model theory context; Show examples of decidable and undecidable fragments inside First order logic, offering an original proof of the following theorem: Any formula of First of order logic is decidable if its prenex normal form is in the following form: ∀x1,…,∀xn∃y1,…,∃ymφ; Presenting a theorem that characterizes the validity of First order logic by the tautologicity of Propositional logic, (...) said result is interesting since immediately arises the doubt of how to conciliate said characterization with Alonzo Church’s Undecidability Theorem for First Order Logic. (shrink)