Tagged Questions
4
votes
2answers
116 views
Sequent calculus and first incompletness theorem
Wikipedia says that sequent calculus is sound and complete (http://en.wikipedia.org/wiki/Sequent_calculus#Properties_of_the_system_LK). Godel first incompleteness theorem says that system capable of ...
5
votes
3answers
299 views
Is the negation of the Gödel sentence always unprovable too?
The incompleteness theorem says that certain theories+deduction system contain at least one sentence (the Gödel sentence "$G$"), which can't be proven (in the system in which it holds).
(i) Is ...
3
votes
3answers
251 views
Aftermath of the incompletness theorem proof
This is somewhat of a minor point about the incompletness theorem, but I'm always a little unsure:
So one proves that there is a formula which is unprovable in the theory of consideration. Okay, at ...
6
votes
1answer
321 views
Can Robinson's Q prove Presburger arithmetic consistent?
I made an assertion in What are some examples of theories stronger than Presburger Arithmetic but weaker than Peano Arithmetic? that Q has higher consistency strength than Pres, Presburger arithmetic; ...
