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Results tagged with metamathematics
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user 11115
the mathematical discipline that applies mathematical methods to the study of mathematical theories themselves.
23
votes
Can infinity shorten proofs a lot?
Consider the following question of Erdos and Hajnal:
Question (Erdos-Hajnal) Is there a finite $K_4$-free graph which, when the edges colored by $2$ colors, always contains a monocolored triangle.
T …
- 32.1k
4
votes
Natural $\Pi_1$ sentence independent of PA
You may look at Shelah's paper
``On logical sentences in PA''.
For a modern exposition of Shelah's work and an alternative example see ``Independence in Arithmetic: The Method of (L, n)-Models''
- 32.1k
4
votes
Is there a compendium of the consistency strength between the most important formal theories?
Another charp, that I found it interesting:
It can be find here: Large cardinals
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