  Let $R$ be a commutative, local, Noetherian ring. In a past article, the
first author developed a theory of $R$-algebras, termed seeds, that can be
mapped to balanced big Cohen-Macaulay $R$-algebras. In prime characteristic
$p$, seeds can be characterized based on the existence of certain
colon-killers, integral extensions of seeds are seeds, tensor products of seeds
are seeds, and the seed property is stable under base change between complete,
local domains. As a result, there exist directed systems of big Cohen-Macaulay
algebras over complete, local domains. In this work, we will show that these
properties can be extended to analogous results in equal characteristic zero.
The primary tool for the extension will be the notion of ultraproducts for
commutative rings as developed by Schoutens and Aschenbrenner.
