in [@Irwin2006] item \[itm:Ltwo\] was replaced by a different but equivalent property.

If $ \mathcal G $ is a projective Fraïssé family of finite $ \mathcal L $-structures and $\mathbb L$ satisfies \[itm:Lone\] and \[itm:Ltwo\], then \[itm:Lthree\] holds if and only if the following extension property holds:

1.  for any $A, B\in \mathcal G $ and epimorphisms $\varphi: B\to A$, $\psi : \mathbb L \to A$ there exists an epimorphism $\chi : \mathbb L \to B$ such that $\varphi\chi =\psi $.

The proof is the same as in [@panagi2017]\*[Lemma 3]{}.

In [@Irwin2006] it is proved that every nonempty, at most countable, projective Fraïssé family of finite $ \mathcal L $-structures has a projective Fraïssé limit, which is unique up to isomorphism.

If $ \mathcal G $ is a class of topological $ \mathcal L $-structures, a *projective sequence* in $ \mathcal G $ is a sequence $(A_n, {\varphi}_n^m)_{n\in {\mathbb N}, m\ge n}$, where:

-   $A_n\in \mathcal G $;

-   $ {\varphi}_n^{n+1}:A_{n+1}\to A_n$ is an epimorphism, for each $n\in {\mathbb N}$;

-   $ {\varphi}_n^m= {\varphi}_n^{n+1}\cdots {\varphi}_{m-1}^m:A_m\to A_n$ for $n<m$, and $ {\varphi}_n^n:A_n\to A_n$ is the identity.

A *projective limit* for such a sequence is a topological $ \mathcal L $-structure $ 