Let $\mathfrak{A}$ be an infinite algebraic structure for not $\omega$-categorical theory. For example, $\mathfrak{A}$ contains an arbitrary functional symbol $f^{(n)}$ and an arbitrary predicate symbol $P^{(m)}$. I am trying to define some fixed point operator (inflationary fixed point or partial fixed point) on $\mathfrak{A}$ such that the values at consecutive steps are different ($X^i \ne X^{i+1}$ for all $i$).
Now I consider pfp (partial fixed point), because the condition $X^i \ne X^{i+1}$ for all $i$ is equal to condition $X^i \ne X^j$ for all $i, j$. It is impossible to construct such ifp-operator.
I tried to use the Ryll-Nardzewski theorem, but did not get any result. Now I try to define some order (linear order, poset, etc.) The idea is to add a next element of order (or finite sequence) at each step of operator construction.
Is this possible? Are there any theorems about this?
Thank you.