Solution of some problems in the arithmetical complexity of first-order   fuzzy logics
  This short paper addresses the open problems left in a previous paper by Franco Montagna and Carles Noguera. Besides giving solutions to these two problems, some clarification concerning the role of the full vocabulary (including functional symbols) in the proofs there given is also discussed. 
F\'elix Bou and Carles Noguera
math.LO