I have difficult to understand the meaning of the notation used by Gödel in the article cited in the title of this post.
You can find it here: http://www.lygeros.org/10552b.pdf
In the second page (p.448) he use the notation $\Gamma_{0, 12}$ that I don't understand. Searching in this website I finally found: Christoffel Symbol - what does a comma mean in the footer?
where is confirmed that the comma means partial derivation. But in that case, the parameter is repeated:
$\Gamma^c_{ab,c}$
In Gödel, it is not.
My question is, is that the same thing?
Do I have to "translate" $\Gamma_{0,12}$ with $\partial_0 \Gamma^0_{12} = \frac{\partial}{\partial x_0}\Gamma^0_{12}$?
Thank you very much for helping, it's the last correction I need to do to my thesis! :)
Andrea
EDIT: The expanded formula is
\begin{align} \Gamma_{0,12} & = \sum_a \Gamma_{12}^a g_{a0} \\ & = \frac{1}{2} \sum_a \sum_k g_{0a} g^{ak} ( \partial_1 g_{k2} + \partial_2 g_{1k} -\partial_k g_{12} ) \\ & = \frac{1}{2} \sum_k g_{0}^k ( \partial_1 g_{k2} + \partial_2 g_{1k} -\partial_k g_{12} ) \\ & = \frac{1}{2} ( \partial_1 g_{02} + \partial_2 g_{10} -\partial_0 g_{12} ) \end{align}