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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 …
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 …
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 …
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 …