# maximal

### adjective

1. the greatest or most complete or best possible

*- maximal expansion*

*- maximum pressure*

### noun

1. (mathematics) The element of a set with the greatest magnitude.

2. (mathematics) 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. (logic) 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.