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the mathematical discipline that applies mathematical methods to the study of mathematical theories themselves.

26 votes
9 answers
5k views

Proofs of Gödel's theorem

I am interested in different contexts in which Gödel's incompleteness theorems arise. Besides traditional Gödelian proof via arithmetization and formalization of liar paradox it may also be obtained …
Sergei Tropanets's user avatar
10 votes
4 answers
1k views

Complete extensions of first order logic (or language)

Lindstrom's theorem states that any extension of first order logic (FOL) more expressible than FOL fails to have either compactness or Lowenheim-Skolem. When I first read Lindstrom's theorem my first …
Sergei Tropanets's user avatar
7 votes
2 answers
871 views

Are computable models sufficient?

What I mean is this. By downward Lowenheim-Skolem theorem, first-order formula Q is a always true iff it is true in every countable structure. But is there some first-order formula Q which is true in …
Sergei Tropanets's user avatar
20 votes
12 answers
10k views

The best text to study both incompleteness theorems

Hi! What text on both incompleteness theorems you would recommend for beginner? Specifically, I'm looking for the text with the following properties: 1) The proofs should be finitistic, in Godel's …