maximal

Of, relating to, or consisting of a maximum.

Being the greatest or highest possible.

An element in an ordered set that is followed by no other.

Of the highest or maximum value, etc.; being a maximum.

Largest, greatest (in magnitude), highest, most.

The element of a set with the greatest magnitude.

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).

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 wff φ, the set contains either φ or ~φ.

the greatest or most complete or best possible