  The immediate past has witnessed an increased amount of interest in local
algorithms, i.e., constant time distributed algorithms. In a recent survey of
the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local
algorithms provide a natural framework that could be used in order to
theoretically control infinite networks in finite time. We study a
comprehensive collection of distributed computing models and prove that if
infinite networks are included in the class of structures investigated, then
every universally halting distributed algorithm is in fact a local algorithm.
To contrast this result, we show that if only finite networks are allowed, then
even very weak distributed computing models can define nonlocal algorithms that
halt everywhere. The investigations in this article continue the studies in the
intersection of logic and distributed computing initiated in (Hella et al.,
PODC 2012) and (Kuusisto, CSL 2013).
