various classes of domains contain universal objects,

i.e. domains which contain any other domain of the given

class as a subdomain (up to isomorphism); such domains can

be used to provide models of the untyped \lambda-calculus.

We will present an inductive probabilistic construction

of bifinite domains and of Scott domains and show that

with probability 1 our construction produces a universal

bifinite domain resp. universal Scott-domain which, moreover,

has a large degree of symmetry. We also develop similar

probabilistic constructions for prime event structures and

for causal sets. The latter have been used as basic models

for discrete space-time in quantum gravity.

Joint work with Dietrich Kuske resp. Guo-Qiang Zhang.

Board Room

Department of Computer Science