I'm reading the lecture on Fraïssé's theorem in Thomas Scanlon's script (p. 115). He mentions that 'if $\tau$ is a relational signature, then HP and AP does imply JEP' but I think I don't get it.
Let $\tau$ consist only of $P$ with arity $1$ and ${\cal K}$ of two $1$-element structures, one in which $P$ is true and one in which it is false. Then ${\cal K}$ satisfies HP and AP (in my opinion) but not JEP.
Where is the mistake?