How can I prove the compactness theorem for sets of sentences?

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The compactness theorem states that a set of sentences T has a model if and only if every finite subset of T has a model. The discussion seeks guidance on proving the opposite direction, emphasizing that while the first direction is clear, the second requires more insight. It is suggested to refer to established proofs in logic textbooks for a clearer understanding. This approach can provide foundational knowledge and techniques necessary for the proof. Engaging with existing literature is recommended to avoid unnecessary complications in the proof process.
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An expression of the compactness theorem for sets of sentences is that: let T be a set of sentences in L. Then T has a model iff every finite subset of T has a model.
Could anyone give me some hints how to prove this?
The first direction is straightforward: every model of T is a model of every subset of T. But what about the opposite direction? Any help is appreciated!
 
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My advice would be to not try to reinvent the wheel, and study the proofs given in any logic textbook.
 

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