In particular we can conceive an abstractive set of which all the members have point-contact at the same event-particle.

It is then easy to prove that there will be no abstractive set with the property of being covered by every abstractive set which it covers.

I state this difficulty at some length because its existence guides the development of our line of argument.

We have got to annex some condition to the root property of being covered by any abstractive set which it covers.

When we look into this question of suitable conditions we find that in addition to event-particles all the other relevant spatial and spatio-temporal abstractive elements can be defined in the same way by suitably varying the conditions.
Accordingly we proceed in a general way suitable for employment beyond event-particles.
Let {sigma} be the name of any condition which some abstractive sets fulfil.