Enderton 2.6.2

Let $\displaystyle T_1$ and $\displaystyle T_2$ be theories (in the same language) such that

(i)$\displaystyle T_1 \subseteq T_2$,

(ii)$\displaystyle T_1$ is complete, and

(iii)$\displaystyle T_2$ is satisfiable. Show that $\displaystyle T_1 = T_2$.

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Before I get started, I need to understand some definitions related to this problem.

(*) AtheoryT is said to becompleteiff for every sentence $\displaystyle \sigma$, either $\displaystyle \sigma \in T$ or $\displaystyle \neg \sigma \in T$.

I am confused with an unsatisfiable theory, where a theory is defined to be a set of sentences closed under logical implication.

The textbook gives an example of an unsatisfiable theory, which is the theory consisting of all sentences of the language. Why is this unsatisfiable theory? Any description or example?

Thank you.