Simple closure
= Simple closure
{title2=$M\preccurlyeq_s N$}
= Simply closed
{synonym}
A <substructure> $M\subseteq N$ is simply closed when each existential <quantifier-free formula> over $M$ realized in $N$ is already realized in $M$. A single quantified variable suffices in the definition; iterating covers finite tuples. This property is also called existential closure in this specified extension. It is weaker than being an <elementary substructure>.