maximal

Short definition from Wiktionary

Adjective

1. 1
   Largest, greatest (in magnitude), highest, most.
2. 2
   Larger than any previous term in the sequence.
3. 3
   Such that no other element is greater (with respect to the given partial order).

Noun

1. 1
   The element of a set with the greatest magnitude.
2. 2
   Said of an ideal of a ring or a filter of a lattice: that it is as large as it can be without being trivial (improper).
3. 3
   Said of a set of well-formed formulas: that it is as large as it can be without being inconsistent; i.e. that for any well-formed formula φ, the set contains either φ or ~φ.