Ideal

Ideal is a particular type of generalized quantifier Q (Q =/= 0) which obeys the condition in (i):

(i) for all X,Y subset E: (X in Q and Y in Q) &lt;=&gt; union(X,Y) in Q

Only N, no N and none of the N are examples of ideals; not all N and at most N are not. The condition in (i) captures the contrast in (ii).

(ii) a Only dogs bark and only dogs run &lt;=&gt; only dogs bark or run b Not all dogs bark and not all dogs run &lt;=/=&gt; not all dogs bark or run

Link
Utrecht Lexicon of Linguistics