Tagged Questions
7
votes
5answers
157 views
Most astonishing applications of compactness theorem outside logic
The compactness theorem has a lot of applications to logic and model theory. I'm looking for applications. I'm looking for theorems in other areas of mathematics which seem at first sight to have ...
5
votes
7answers
422 views
What are some examples of subtle logical pitfalls?
Here's an example:
Demonstrating that the assumption $A=B$ leads to a true statement is a vacuous truth. In order the show that $A=B$, prove that the difference $\Delta =A-B$ is zero. The subtle ...
15
votes
5answers
574 views
What are the theorems of mathematics proved by a computer so far?
By theorems, I mean the ones you can find in an undergraduate course of mathematics, not the ones you can find in a textbook of automated proofs.
I mean by "proved by a computer" that an existing ...
3
votes
1answer
164 views
List of important and influential publications in logic
Wikipedia surprisingly does not contain a good list. Under philosophy of mathematics it is rather vacant too. A graduate level list is here, but I was curious more about the most influential papers. ...
3
votes
1answer
135 views
A Formal and Precise treatment of Simplification?
I am looking to gain a deeper understanding of, and increase my own skill in "Mathematical Simplification". But I've been finding the concept overly vague and haven't been able to find any good ...
3
votes
1answer
319 views
Short open problems or undecidable statements in ZFC
I guess Goldbach's conjecture is a good example of a short open problem in number theory, and "Goodstein sequences reach 1" is a good example of a statement undecidable from first-order Peano ...
24
votes
10answers
4k views
Good books on mathematical logic?
I just started to learn mathematical logic. I'm a graduate student. I need a book with relatively more examples. Any recommendation?
