  Dimension is a standard and well-studied measure of complexity of posets.
Recent research has provided many new upper bounds on the dimension for various
structurally restricted classes of posets. Bounded dimension gives a succinct
representation of the poset, admitting constant response time for queries of
the form "is $x<y$?". This application motivates looking for stronger notions
of dimension, possibly leading to succinct representations for more general
classes of posets. We focus on two: boolean dimension, introduced in the 1980s
and revisited in recent research, and local dimension, a very new one. We
determine precisely which values of dimension/boolean dimension/local dimension
imply that the two other parameters are bounded.
