I've been reading about formal systems and formal logic (gödel's incompleteness theorem, lambda calculus, curryhoward and such) since they were named and more or less explained in a book I was reading but I'd like to read something more specific about these topics since I found them extremely interesting.
A quick search showed me that this is a very wide field spacing from proof theory to mathematical logic and many other topics so I'm a bit confused about what should I read, can someone suggest me a good book on these topics?
Thanks in advance!
Alessandro
formal logic and similar topics
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 Joined: Wed Apr 24, 2013 1:33 am UTC
formal logic and similar topics
The primary reason Bourbaki stopped writing books was the realization that Lang was one single person.
Re: formal logic and similar topics
What are you interested in?
For a good and thorough introduction to lambda calculi from a computer science pointofview I recommend Types and Programming Languages by Benjamin C. Pierce. It has rigorous proofs of the basic theorems in this area and very readable. It also talks about the application of type theory to real world programming languages.
Unfortunately I don't know a good intro book to mathematical logic.
For a good and thorough introduction to lambda calculi from a computer science pointofview I recommend Types and Programming Languages by Benjamin C. Pierce. It has rigorous proofs of the basic theorems in this area and very readable. It also talks about the application of type theory to real world programming languages.
Unfortunately I don't know a good intro book to mathematical logic.

 Posts: 109
 Joined: Wed Apr 24, 2013 1:33 am UTC
Re: formal logic and similar topics
I was more interested in a mathematical point of view than a computer science one even though that book sounds very interesting.
The problem is that I've read about Gödel and formal systems but I don't know exactly what is the field of mathematics dealing with this things so I don't know what should I be looking for a more indepth explanation
The problem is that I've read about Gödel and formal systems but I don't know exactly what is the field of mathematics dealing with this things so I don't know what should I be looking for a more indepth explanation
The primary reason Bourbaki stopped writing books was the realization that Lang was one single person.
Re: formal logic and similar topics
Gödel's incompleteness theorems belong to the topic of mathematical logic. You generally need some proof theory and model theory to understand the arguments.

 Posts: 109
 Joined: Wed Apr 24, 2013 1:33 am UTC
Re: formal logic and similar topics
Thanks for the reply, I'll look for an introductory book about mathematical logic then, but I'm open to suggestions if someone has read such a book and found it well written!
The primary reason Bourbaki stopped writing books was the realization that Lang was one single person.
Re: formal logic and similar topics
Marker's "Model Theory" is the textbook I used in undergraduate. It's decent.
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 Posts: 109
 Joined: Wed Apr 24, 2013 1:33 am UTC
Re: formal logic and similar topics
after reading plenty of reviews and similar questions on mathoverflow I think I'll buy one of these 2:
Mathematical Logic by Joseph R. Shoenfield
Introduction to Metamathematics by Stephen C. Kleene
since they are apparently both very well known and "classics" in the field, still I'd like to know if someone has read one (or both) of them and can give me an opinion. (I cannot buy both right now, but I could start with one and buy the other later if it's worth)
edit:
there's another book from Kleene, called Mathematical Logic, but I found much more reccomendations for "Introduction to Metamathematics", if someone has read both of them could explain me what's different in the 2 books?
Mathematical Logic by Joseph R. Shoenfield
Introduction to Metamathematics by Stephen C. Kleene
since they are apparently both very well known and "classics" in the field, still I'd like to know if someone has read one (or both) of them and can give me an opinion. (I cannot buy both right now, but I could start with one and buy the other later if it's worth)
edit:
there's another book from Kleene, called Mathematical Logic, but I found much more reccomendations for "Introduction to Metamathematics", if someone has read both of them could explain me what's different in the 2 books?
The primary reason Bourbaki stopped writing books was the realization that Lang was one single person.
 Forest Goose
 Posts: 377
 Joined: Sat May 18, 2013 9:27 am UTC
Re: formal logic and similar topics
The linked book, by Hedman, is interesting and readable (I like it):
http://www.amazon.com/FirstCourseLogi ... 0198529813
Logic and Structure, by Van Dalen, isn't bad for an intro text on logic.
Model Theory, by David Marker, also isn't bad (though, personally, I didn't enjoy it...)
If none of these are what you are looking for, I have a whole library of logic/compsci books at home, I'm sure I could find something better there (I'm away for a few days right now).
http://www.amazon.com/FirstCourseLogi ... 0198529813
Logic and Structure, by Van Dalen, isn't bad for an intro text on logic.
Model Theory, by David Marker, also isn't bad (though, personally, I didn't enjoy it...)
If none of these are what you are looking for, I have a whole library of logic/compsci books at home, I'm sure I could find something better there (I'm away for a few days right now).
Forest Goose: A rare, but wily, form of goose; best known for dropping on unsuspecting hikers, from trees, to steal sweets.
Re: formal logic and similar topics
korona wrote:Gödel's incompleteness theorems belong to the topic of mathematical logic. You generally need some proof theory and model theory to understand the arguments.
That being said, Raymond Smullyan has written a series of recreational logic books that dive into the heart of incompleteness, the SIcalculus, and other deep fields. While they may lack the rigor and extensibility that you'll see in a formal textbook, they make up for it in readability.
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