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Results tagged with metamathematics
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user 12705
the mathematical discipline that applies mathematical methods to the study of mathematical theories themselves.
10
votes
Existential statement without witness
$\def\epn{\mathrm{EP}_\mathbb N}\def\dp{\mathrm{DP}}$When a theory $T$ (with a distinguished definable set of “natural numbers” satisfying a suitable minimal arithmetic) has the property in the questi …
- 47.1k
24
votes
Accepted
Are there examples of nonconstructive metaproofs?
In theory, David’s answer is correct. Nevertheless, in practice it is perfectly possible to prove the existence of a proof non-constructively (such as by manipulating models and then appealing to the …
- 47.1k
4
votes
Is every recursively axiomatizable and consistent theory interpretable in the true arithmeti...
The other answers are enough to answer the question as given. However, let me point out for the record that using the arithmetized completeness theorem over PA is quite an overkill. We can make do wit …
- 47.1k