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Oct
4
awarded  Popular Question
Oct
31
awarded  Autobiographer
Dec
29
comment Proof of the Compactness Theorem for Propositional Logic
I accepted your answer but I still don't get it. There are too many symbols to keep in my head at the same time. :) I'll keep trying.
Dec
29
awarded  Scholar
Dec
29
accepted Proof of the Compactness Theorem for Propositional Logic
Dec
29
comment Proof of the Compactness Theorem for Propositional Logic
Ok, I have to admit your proof is too hard for me to digest. I think the basic idea is to say that every formula $\phi$ has only finitely many propositional variables. Let $n$ be that number. Then $\phi$ belongs to $S_n$, which has a model. So there is a model for every $\phi$ in $S$. Therefore, $S$ has a model.
Dec
29
awarded  Supporter
Dec
29
comment Proof of the Compactness Theorem for Propositional Logic
Sorry, I can't access the page you linked, none of the images are loaded due to some authorization error.
Dec
27
comment Proof of the Compactness Theorem for Propositional Logic
In your 3rd paragraph, how do you decide if $T_1$ is infinite?
Dec
27
awarded  Student
Dec
27
comment Proof of the Compactness Theorem for Propositional Logic
Thanks, you're right. I read the FAQ after posting the question.
Dec
26
asked Proof of the Compactness Theorem for Propositional Logic