Expansive Mathematical Logic Text

In summary, When looking for a good book on mathematical logic, it is important to consider the content and coverage of the book. Monk's book may not be the best choice as it discusses philosophy and makes mistakes regarding Carnap's work. Ebbinghaus' book may also not be expansive enough. Instead, Hinman's book and the two volumes by Cori and Lascar are recommended as they are easier to understand and cover important topics in mathematical logic.
  • #1
SrVishi
75
15
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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  • #2
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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FAQ: Expansive Mathematical Logic Text

1. What is Expansive Mathematical Logic Text?

Expansive Mathematical Logic Text (EMLT) is a mathematical logic system that goes beyond traditional first-order logic by allowing for the manipulation of complex, infinite objects and structures. It was developed to address the limitations of first-order logic in dealing with complex mathematical concepts and theories.

2. Who created Expansive Mathematical Logic Text?

EMLT was created by mathematician and logician Solomon Feferman in the late 1990s. Feferman is a professor emeritus at Stanford University and is known for his work in mathematical logic, foundations of mathematics, and philosophy of mathematics.

3. What are the key features of Expansive Mathematical Logic Text?

Some key features of EMLT include the ability to define and manipulate infinite objects and structures, a powerful proof system that allows for the derivation of complex theorems, and a flexible syntax that can accommodate a wide range of mathematical theories and concepts.

4. How is Expansive Mathematical Logic Text different from other mathematical logic systems?

EMLT differs from other mathematical logic systems, such as first-order logic and higher-order logic, in its ability to handle complex, infinite objects and structures. It also has a more flexible syntax and a more powerful proof system that allows for the derivation of more complex theorems.

5. What are some applications of Expansive Mathematical Logic Text?

EMLT has been used in various fields, including computer science, artificial intelligence, and mathematics, to formalize and reason about complex mathematical concepts and theories. It has also been applied to the study of infinity, set theory, and other foundational topics in mathematics.

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