## New answers tagged proof-theory

7
votes

Accepted

### Consistency in pure type systems

I think this awkwardness is coming from your “principle of constants”, which is not standard, and doesn’t seem justified by the motivation you give.
You say it’s meant to correspond to the practice (...

4
votes

### Has Apéry's proof of the irrationality of $\zeta(3)$ ever been used to prove the irrationality of other constants?

I also want to mention the formula (origin unknown)
$$\dfrac{56\zeta(3)}{3}=\sum_{n\ge1}\dfrac{64^n}{n^3D_nD_{n-1}}\;,$$
where $D_n=W_4(2n)$ is the $n$th Domb number, equivalent to the continued ...

21
votes

Accepted

### Has Apéry's proof of the irrationality of $\zeta(3)$ ever been used to prove the irrationality of other constants?

The proof of irrationality of $\displaystyle\sum_{n=0}^{+\infty}\frac1{F_n}$ (where $F_n$ is the $n$-th Fibonacci number) by RIchard André-Jeannin is an adaptation of the original Apery's proof of the ...

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