Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are probably classes of something, but i don't know their name and i wasn't able to find something i can understand (I read about hierachies, but hierachies of what and, in which field of mathematics?)
I hope someone can give me an easy explaination of these things (classes?), how they are related, in which field(s) of mathematics these concepts appear and a formal definition (or a link).
Thanks in advance. and I apologize for errors (I'm using a translator).
What is the meaning of the upper index $0$? In the logic use of this notation $\Sigma_n^1$ is the hieracy of the formulas in the language of second-order arithmetic. Intuitively I could think that the hierchies $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$ are the hierachies of the formulas in the language of $(i−1)$-order arithmetic..probably I'm wrong but how this index is linked with other fields?