Expansive Mathematical Logic Text

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SUMMARY

The discussion centers on recommendations for expansive mathematical logic texts, specifically comparing works by Ebinghaus, Monk, and Schoenfield. The consensus indicates that Monk's book is inadequate due to its philosophical biases and inaccuracies regarding Carnap's theories. In contrast, Ebinghaus is deemed less expansive, while Hinman's book is favored for its clarity. Additionally, the two-volume series by Cori and Lascar is recommended as an easier alternative for foundational concepts in mathematical logic.

PREREQUISITES
  • Familiarity with basic mathematical logic concepts
  • Understanding of philosophical implications in mathematics
  • Knowledge of Carnap's internal and external language
  • Experience with set theory as outlined in Jech's work
NEXT STEPS
  • Research Hinman's book on mathematical logic for comprehensive coverage
  • Explore Cori and Lascar's two-volume series for foundational understanding
  • Study Schoenfield's text for a broader perspective on mathematical logic
  • Investigate the philosophical aspects of mathematical logic, particularly Carnap's theories
USEFUL FOR

Students and educators in mathematics, particularly those focusing on mathematical logic, philosophy of mathematics, and foundational theories. This discussion is beneficial for anyone seeking to deepen their understanding of expansive mathematical logic texts.

SrVishi
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Hello, I want to start learning mathematical logic. I was wondering what would be a good "expansive" mathematical logic book that covers as much material as possible. My school has books by both Ebinghaus (et. al) and Monk. Are these good? I've heard good things about Schoenfield, but I was wondering how they compare to the aforementioned books. Thanks in advance for any response. [Note: I am already planning on going through Jech's Set theory, along with Kunen's books and Model Theory by Chang]
 
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Monk doesn't look good and Ebbinghaus doesn't look expansive.

Why does Monk not look good? He talks about philosophy in the preface and mentions that he wrote a book about platonism and formalism, topics in the philosophy of math, but he seems unfamiliar with Carnap because he makes a mistake that Carnap wrote about in 1950. Monk's book is from 1967 and I think he should have known about Carnap's concept of internal and external language. If anything, I read his preface as a defense against exactly this criticism, that he goes against Carnap. It's not a convincing defense, it was wrong when he wrote it and it is still wrong today.
 
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