2
votes
1answer
194 views

Good book for logic self-study

I know a similar question has already been asked, but can anyone suggest a good book on mathematical logic that includes answers to exercises? I am looking for something that is conducive to ...
1
vote
3answers
119 views

Paradoxes without self-reference?

Most paradoxes involves self-reference, the only exception known to me is Yablo's paradox, however it is still debated if it is really without self-reference. So, I was wondering, are there other ...
7
votes
5answers
389 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
536 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 ...
13
votes
5answers
649 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
230 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
148 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
367 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 ...
25
votes
10answers
8k 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?