Ultimate
is a canonical inner model program proposed by Woodin (2017) for accommodating very
strong large cardinals. It is intended to extend
Gödel's constructible universe
beyond the range of currently constructed fine-structural
inner models while retaining a comparably rigid theory.
Ultimate
is a program and conjectural model rather than a completed construction in the full
proposed generality. Its proposed existence and relation to the set-theoretic universe
are formulated in the Ultimate L conjecture.