Luigi Santocanale:  Free $\mu$-lattices.

ABSTRACT:
A $\mu$-lattice is a lattice with the property that every unary
polynomial with coefficients in it has both a least and a greatest
fix-point.

In this talk I'll define the category of $\mu$-lattices and for a
given partially ordered set $P$ I'll show how to construct a
$\mu$-lattice ${\cal J}_{P}$ by means of games.  Also I'll discuss how
to prove that the order relation of ${\cal J}_{P}$ is decidable, given
that the order relation of $P$ is decidable.

The $\mu$-lattice ${\cal J}_{P}$ is actually free over the partially
ordered set $P$.  I'll discuss the proof of freeness and explain why
it suggests circular proofs as good models of proofs.