Elementary Logic Book: Complete Completeness Theorem Coverage

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SUMMARY

The discussion centers on the search for an elementary logic book that thoroughly covers Gödel's completeness theorem. Participants clarify that Gödel's completeness theorem is distinct from his incompleteness theorems and suggest that any good introductory text on formal logic should include it. Notably, Nagel and Neumann's "Gödel's Proof" is recommended as one of the simplest resources available. The conversation emphasizes the need for clarity regarding which completeness theorem is being referenced, as there are multiple theorems across different contexts.

PREREQUISITES
  • Understanding of Gödel's completeness theorem
  • Familiarity with formal logic concepts
  • Knowledge of Gödel's incompleteness theorems
  • Basic comprehension of mathematical proofs
NEXT STEPS
  • Research introductory texts on formal logic that include Gödel's completeness theorem
  • Explore Nagel and Neumann's "Gödel's Proof" for a simplified explanation
  • Investigate other completeness theorems in various logical contexts
  • Study the implications of Gödel's theorems on mathematical logic
USEFUL FOR

Students of formal logic, educators seeking teaching materials, and anyone interested in the foundational aspects of 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.
 

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