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First order logic: "consistency," "compactness"?

Consistency: A set $\Sigma\subseteq\text{WFF}$ is consistent iff there is no $\varphi\in\text{WFF}$ such that $\Sigma\vdash\varphi$ and $\Sigma\vdash\lnot\varphi$.

Compactness: A set $\Sigma$ is consistent iff every finite $\Sigma_0\subseteq\Sigma$ is consistent.

I have read through these definitions, however I still feel like I do not understand them. Can someone respond and break them down for me in simpler terms? I feel more confident in my abilities if I understand them to the fullest and their application.

Thank you

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    What definitions? They are missing.2012-12-10
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    I don't think that a general explanation of consistency and compactness is the sort of question that the FAQ for the site asks for. In particular, it is hard to see that there is a correct answer to the question, such as it is. The FAQ says, " If you can imagine an entire book that answers your question, you’re asking too much." For that reason, I voted to close. However, the question could be improved by asking about the specific thing that you would like to know about.2012-12-10
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    could you explain them further then the definitions?2012-12-10

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