|Jun6-10, 04:28 PM||#1|
compactness theorem proof
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!
|Jun6-10, 06:26 PM||#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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