compactness theorem proof


by rainwyz0706
Tags: compactness, proof, theorem
rainwyz0706
rainwyz0706 is offline
#1
Jun6-10, 04:28 PM
P: 36
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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JSuarez
JSuarez is offline
#2
Jun6-10, 06:26 PM
P: 403
My advice would be to not try to reinvent the wheel, and study the proofs given in any logic textbook.


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