Let $P$ be a property of finitely presented algebra preserved under isomorphism. $P$ is called Markov if there exists a finitely presented algebra $L_1$ satisfying $P$ and a finitely presented algebra $L_2$ which can not be embedded in a finitely presented algebra satisfying $P$. For example, every non-trivial property $P$ preserved by taking subalgebras is Markov such as abelian, nilpotent, solvable and free. This concept has been studied for Lie algebras as well.
The question is: Let take algebra $L$ which is not Schreier variety. Is it true to say that the freeness in not a Markov property for given algebra $L$? How can we investigate Markov property for such algebras? Should we at first find those properties which are Markov and then investigate their decidabilities?