Elementary Logic Book: Complete Completeness Theorem Coverage

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Discussion Overview

The discussion revolves around the search for an elementary logic book that thoroughly covers the completeness theorem. Participants explore the meaning of the completeness theorem and its relation to Gödel's work, as well as the appropriateness of various texts for this topic.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant seeks a logic book that completely covers the completeness theorem.
  • Another participant questions whether the completeness theorem refers to Gödel's theorem, suggesting that an elementary logic book may not adequately cover it.
  • A participant clarifies that Gödel indeed proved a completeness theorem in addition to his incompleteness theorems, noting the potential for multiple completeness theorems in different contexts.
  • There is a suggestion that Gödel's completeness theorem should be included in any good introductory text on formal logic, distinguishing it from texts focused on proofs in mathematics.
  • The original poster confirms they are referring to Gödel's completeness theorem and requests recommendations for the most basic introductory texts available.

Areas of Agreement / Disagreement

Participants express differing views on what is meant by the completeness theorem and whether it can be adequately covered in an elementary logic book. There is no consensus on specific texts or the sufficiency of coverage.

Contextual Notes

Uncertainty exists regarding which completeness theorem is being referenced and the definitions of "elementary" and "basic" in the context of logic texts.

tgt
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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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