  This short note presents a new relation between coherent spaces and
finiteness spaces. This takes the form of a functor from COH to FIN commuting
with the additive and multiplicative structure of linear logic. What makes this
correspondence possible and conceptually interesting is the use of the infinite
Ramsey theorem. Along the way, the question of the cardinality of the
collection of finiteness spaces on N is answered. Basic knowledge about
coherent spaces and finiteness spaces is assumed.
