finiteness

Regarding the last message of Bill on finiteness and the answer of Vickers, I would like to point out that the 25 years old reference of Bill should be the one at the bottom of page 14 of lesson 3 of 1972 Perugia Notes. In other words, the L he is suggesting should be the internalization of the following description: L consists of those ideals T : N---->Omega such that for all n Tn = Inf{Tm | m > n}. The precise meaning of this definition is explained in the given reference, as well as in Bill's messages. I hope that this is correct. Aurelio Carboni