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Results tagged with metamathematics
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user 23141
the mathematical discipline that applies mathematical methods to the study of mathematical theories themselves.
3
votes
How can you formalize the metamathematics conventionally used to state Godel’s theorem?
I think this question is clearly asking for provability logic. This is the basic modal logic K with the additional axiom
$$\square(\square A \to A) \to \square A.$$
"$\square A$" is interpreted as " …
- 42.8k
12
votes
Which kind of foundation are mathematicians using when proving metatheorems?
One direction could go like this. Let ${\rm ZFC}^+$ be the theory in the language of set theory augmented by a constant symbol ${\bf M}$ with the axioms
$\bullet$ every axiom of ${\rm ZFC}$
$\bullet …
- 42.8k
4
votes
How necessary is Godel's Condensation Lemma
It's been 25 years since I struggled through it, but I clearly remember that Godel's book Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory g …
- 42.8k
6
votes
Formal proof of Con(ZFC) => Con(ZFC + not CH) in ZFC
The other answers are perfectly correct, but I'd like to add that the implication Con(ZFC) $\to $Con(ZFC + $\neg$CH) is not only provable in ZFC, it is provable in Peano arithmetic. I consider this a …
- 42.8k