## LPi Logic with Fixed Points

We study a system, $\mu$L$\Pi$, obtained by an expansion of L$\Pi$ logic with fixed points connectives. The first main result of the paper is that $\mu$L$\Pi$ is standard complete, i.e. complete with regard to the unit interval of real numbers endowed with a suitable structure.

We also prove that the class of algebras which forms algebraic semantics for this logic is generated, as a variety, by its linearly ordered members and that they are precisely the interval algebras of real closed fields. This correspondence is extended to a categorical equivalence between the whole category of those algebras and another category naturally arising from real closed fields.

Finally, we show that this logic enjoys implicative interpolation.

## muMV-algebras: an approach to fixed points in Lukasiewicz logic

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 and MV$_\Delta$ algebras. Using methods from the two known extensions we derive a number of results about $\mu$MV-algebras; among others: subdirect representation, standard completeness, amalgamation property and a description of the free algebra.

muMV-algebras: an approach to fixed points in Lukasiewicz logic