Hello I am having difficulty with this question, I am not even sure what strategy one would go about proving something like this:
Suppose $L$ is a language which includes an infinite list $c_1,c_2,\cdots$ of constant symbols. Let $\Gamma$ be a set of sentences $\Gamma = \{c_i \neq c_j | i,j\in N, i < j\}$. Let A be a sentence such that $\Gamma \Rightarrow A$. Prove that $A$ has a finite model.
I am not sure whether I would prove this via a contradiction (i.e., assume $A$ has an infinite model, or if I show a finite model that works or some how assume that we can have an infinite model and then use some sort of compactness to show it can be finite. I am a little all over the place with this question, please any help would be great!