  Given a poset $P$, a family $F$ of elements in the Boolean lattice is said to
be $P$-saturated if (1) $F$ contains no copy of $P$ as a subposet and (2) every
proper superset of $F$ contains a copy of $P$ as a subposet. The maximum size
of a $P$-saturated family is denoted by $La(n,P)$, which has been studied for a
number of choices of $P$. The minimum size of a $P$-saturated family,
$sat(n,P)$, was introduced by Gerbner et al. (2013), and parallels the deep
literature on the saturation function for graphs.
  We introduce and study the concept of saturation for induced subposets. As
opposed to induced saturation in graphs, the above definition of saturation for
posets extends naturally to the induced setting. We give several exact results
and a number of bounds on the induced saturation number for several small
posets. We also use a transformation to the biclique cover problem to prove a
logarithmic lower bound for a rich infinite family of target posets.
