We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval . This result also implies…
We prove that the $n$-generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the $n$-generated free MV$^{(n)}$-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV${}^{(n)}$-algebras…
We study an expansion of MV-algebras, called $\mu$MV-algebras, in which minimum and maximum fixed points are definable. The first result is that $\mu$MV-algebras are term-wise equivalent to divisible MV$_\Delta$ algebras, i.e. a combination of two known MV-algebras expansion: divisible MV-algebras…
A new class of $MV$-algebras with product, called L$\Pi_q$-algebras, has been introduced. In these algebras, the discontinuous product residuation $\to_\pi$ is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need ofexpressiveness…