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Compactness theorem proof

  1. Jun 6, 2010 #1
    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!
  2. jcsd
  3. Jun 6, 2010 #2
    My advice would be to not try to reinvent the wheel, and study the proofs given in any logic textbook.
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