  Let $R$ be a commutative, indecomposable ring with identity and $(P,\le)$ a
partially ordered set. Let $FI(P)$ denote the finitary incidence algebra of
$(P,\le)$ over $R$. We will show that, in most cases, local automorphisms of
$FI(P)$ are actually $R$-algebra automorphisms. In fact, the existence of local
automorphisms which fail to be $R$-algebra automorphisms will depend on the
chosen model of set theory and will require the existence of measurable
cardinals. We will discuss local automorphisms of cartesian products as a
special case in preparation of the general result.
