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Possible Duplicate:
What is the difference between Gödel's Completeness and Incompleteness Theorems?
what is the relationship between ZFC and first-order logic?

I am a bit confused by a few things that I have read recently.

I have read that ZFC is a first order theory and that any part of mathematics can be expressed in ZFC. Now I know that first order logic is complete, however this would seem to contradict the incompleteness theorems (with I have a basic understanding of). I was wondering where I have gone wrong?

Thanks very much for any help (sorry for the silly question)

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    Re-read the incompleteness theorems ;)2012-10-03
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    Long story short: "complete" has at least two meanings.2012-10-03
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    First order logic is a complete theory (I think). But ZFC consists of first order logic plus the relation $\epsilon$ and the axioms of set theory and is incomplete.2012-10-03
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    Proof once again the Gödel was the greatest logician ever: not only did he prove an amazing theorem in his dissertation, but about two years later he proved its negation!2012-10-03
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    @AndréNicolas I slap my forehead and stad corrected.2012-10-03
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    http://math.stackexchange.com/questions/14709/what-is-the-difference-between-godels-completeness-and-incompleteness-theorems/14710#147102012-10-03

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