## Advances in the theory of muLPi algebras

Recently an expansion of $$\rm L {\rm\Pi\frac{1}{2}}$$ logic with fixed points has been considered. In the present work we study the algebraic semantics of this logic, namely $$\mu L\Pi$$ algebras, from algebraic, model theoretic and computational standpoints.
We provide a characterisation of free $$\mu L\Pi$$ algebras as a family of particular functions from $$[0,1]^{n}$$ to $$[0,1]$$.  We show that the first-order theory of linearly ordered $$\mu L\Pi$$-algebras enjoys quantifier elimination, being, more precisely, the model completion of the theory of linearly ordered $$\rm L {\rm\Pi\frac{1}{2}}$$ algebras. Furthermore, we give a functional representation of any $$\rm L {\rm\Pi\frac{1}{2}}$$ algebra in the style of Di Nola Theorem for MV-algebras and finally we prove that the equational theory of $$\mu L\Pi$$ algebras is in PSPACE.

Advances in the theory of muLPi algebras