  Recent results of Bucciarelli show that the semilattice of degrees of
parallelism of first-order boolean functions in PCF has both infinite chains
and infinite antichains. By considering a simple subclass of Sieber's
sequentiality relations, we identify levels in the semilattice and derive
inexpressibility results concerning functions on different levels. This allows
us to further explore the structure of the semilattice of degrees of
parallelism: we identify semilattices characterized by simple level properties,
and show the existence of new infinite hierarchies which are in a certain sense
natural with respect to the levels.
