Force recurrence of semigroup actions.

We investigate the sets of countable discrete semigroups that force recurrence, that is, the recurrent properties of a point along a subset of a countable semigroup action. We show that a subset of a monoid forces recurrence (resp., forces minimality) if and only if it contains a broken IP-set (resp., broken syndetic set), and forces infinite recurrence implies it is contains a broken infinite IP-sets. As an example, we show that every subset with positive upper Banach density of infinite countable amenable groups forces infinite recurrence. [ABSTRACT FROM AUTHOR]