Elementary Logic Book: Complete Completeness Theorem Coverage

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An elementary logic book that thoroughly covers Gödel's completeness theorem is sought after in the discussion. Gödel's completeness theorem is distinct from his incompleteness theorems and is typically included in introductory texts on formal logic. Recommendations include Nagel and Neumann's "Gödel's Proof" for its simplicity. The conversation highlights the need for clarity on which completeness theorem is being referenced, as there are multiple theorems in different contexts. Overall, a good introductory text on formal logic should suffice for understanding Gödel's completeness theorem.
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Need an elementary logic book that completely covers the completeness theorem (no pun intended).
 
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What do you mean by the "completeness theorem"? I know of Goedel's incompleteness theorem. If that is what you mean, I honestly don't think an elementary logic book could! In my opinion, Nagel and Neumann's book "Goedel's Proof" is probably the simplest.
 
Gödel proved a completeness theorem in addition to his two incompleteness theorems for logic. There are probably other 'completness theorem's too both in logic and in other contexts, so it's not clear that's the one the OP means.

If the OP does mean Gödel's completeness theorem, I imagine it should be in just about any good introductory text on formal logic. (i.e. a text meant to teach the discipline of formal logic, rather than an 'introduction to proofs in mathematics'-type book)
 
Hurkyl said:
Gödel proved a completeness theorem in addition to his two incompleteness theorems for logic. There are probably other 'completness theorem's too both in logic and in other contexts, so it's not clear that's the one the OP means.

If the OP does mean Gödel's completeness theorem, I imagine it should be in just about any good introductory text on formal logic. (i.e. a text meant to teach the discipline of formal logic, rather than an 'introduction to proofs in mathematics'-type book)

Yes, Godel's completeness theorem. Any specific ones? I am looking for the most basic one available.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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