  In this paper, we construct an infinitary variant of the relational model of
linear logic, where the exponential modality is interpreted as the set of
finite or countable multisets. We explain how to interpret in this model the
fixpoint operator Y as a Conway operator alternatively defined in an inductive
or a coinductive way. We then extend the relational semantics with a notion of
color or priority in the sense of parity games. This extension enables us to
define a new fixpoint operator Y combining both inductive and coinductive
policies. We conclude the paper by sketching the connection between the
resulting model of lambda-calculus with recursion and higher-order
model-checking.
