  The aim of this paper is to study a deep connection between local cohomology
annihilators and Macaulayfication and arithmetic Macaulayfication over a local
ring. Local cohomology annihilators appear through the notion of p-standard
system of parameters. For a local ring, we prove an equivalence of the
existence of Macaulayfications; the existence of a p-standard system of
parameters; being a quotient of a Cohen-Macaulay local ring; and the
verification of Faltings' Annihilator theorem. For a finitely generated module
which is unmixed and faithful, we prove an equivalence of the existence of an
arithmetic Macaulayfication and the existence of a p-standard system of
parameters; and both are proved to be equivalent to the existence of an
arithmetic Macaulayfication on the ground ring. A connection between
Macaulayfication and universal catenaricity is also discussed.
