Free monadic Tarski and MMI3-algebras

Abstract

MMI3-algebras are a generalization of the monadic Tarski algebras as defined by A. Monteiro and L. Iturrioz, and a particular case of the MMIn+1-algebras defined by A. Figallo. They can also be seen as monadic three-valued £ukasiewicz algebras without a first element. By using this point of view, and the free monadic extensions, we construct the free MMI3-algebras on a finite number of generators, and indicate the coordinates of the generators. As a byproduct, we also obtain a construction of the free monadic Tarski algebras.