I say that an abstractive set is '{sigma}-prime' when it has the two properties, (i) that it satisfies the condition {sigma} and (ii) that it is covered by every abstractive set which both is covered by it and satisfies the condition {sigma}.
In other words you cannot get any abstractive set satisfying the condition {sigma} which exhibits intrinsic character more simple than that of a {sigma}-prime.
There are also the correlative abstractive sets which I call the sets of {sigma}-antiprimes.

An abstractive set is a {sigma}-antiprime when it has the two properties, (i) that it satisfies the condition {sigma} and (ii) that it covers every abstractive set which both covers it and satisfies the condition {sigma}.

In other words you cannot get any abstractive set satisfying the condition {sigma} which exhibits an intrinsic character more complex than that of a {sigma}-antiprime.
The intrinsic character of a {sigma}-prime has a certain minimum of fullness among those abstractive sets which are subject to the condition of satisfying {sigma}; whereas the intrinsic character of a {sigma}-antiprime has a corresponding maximum of fullness, and includes all it can in the circumstances.
Let us first consider what help the notion of antiprimes could give us in the definition of moments which we gave in the last lecture.

Let the condition {sigma} be the property of being a class whose members are all durations.

An abstractive set which satisfies this condition is thus an abstractive set composed wholly of durations.