I'm stuck with this problem:
$L$ is first-order language with identity and $L_q$ a language obtained by adding to $L$ the quantifier $Q$. If $P$ is a formula and $x$ a variable, $QxP$ is a formula of $L_q$. If $A$ is a $L_q$-structure, then $A\vDash QxP$ if and only if $\#\left(\{a \in |A| : A\vDash P[a]\}\right)>\aleph_0$.
I have to show that there exists $T\subset\operatorname{For}(L_q)$ of cardinal superior to $\aleph_0$ such that T does not have a model and every finite subset has a model
Any ideas??
thanks!