Definition (satisfiability): a set $\Gamma$ of formulas of a first order language is satisfiable if there exist a structure $S$, a Boolean algebra $B$ and an evaluation function $V$ such that $V(C)=1_B$ for every formula $C \in \Gamma$.
Theorem (Compactness): a set $\Gamma$ of formulas of a first order language is satisfiable if and only if every finite subset of $\Gamma$ is satisfiable.
I tried to prove the Compactness theorem in a constructive way but I didn't succeed, so now I wonder if the Compactness theorem constructively implies some other statement that cannot be proved in constructive mathematics (an intuitionistic taboo). Can someone help me?
