1 ZFC could be formulated as First order logic.

2 Gödel's Completeness theorem is a theorem within ZFC.

3 I think a lot of books about set theory is implicitly assuming Gödel's completeness theorem without proof.First I assume Gödel's completeness theorem without proof, after that will it be pfoofed?

Is it correct? please give me your opinion?


closed as unclear what you're asking by Andrés E. Caicedo, Eric Wofsey, Claude Leibovici, choco_addicted, John B Apr 7 '16 at 7:05

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  • $\begingroup$ ZF is a theory in first-order logic. So, the model- and proof-theory of first-order logic apply to ZF. Is this what you are asking? $\endgroup$ – Noah Schweber Mar 31 '16 at 1:25
  • $\begingroup$ @Noah Schweber thank you for your comment. yes, but before I apply it,semantically proof result about the model- and proof-theory of first-order logic within ZFC. $\endgroup$ – tarou Mar 31 '16 at 1:33
  • $\begingroup$ I don't understand what you mean. $\endgroup$ – Noah Schweber Mar 31 '16 at 1:33
  • $\begingroup$ What kind of theory did result about the model- and proof-theory of first-order logic proof? $\endgroup$ – tarou Mar 31 '16 at 1:35
  • $\begingroup$ @tarou Are you using some kind of online translator? It's pretty difficult to understand what you're asking. If english is not your first language, don't be afraid and type it out in your native language. Many guys here will translate it for you. $\endgroup$ – YoTengoUnLCD Mar 31 '16 at 3:02