What's meta-arithmetic?

Question

I am not able to find a definition of meta-arithmetic. Thus I am asking here this

Question. Do you know what's means meta-arithmetic? If do you know it, can you explain me in easy words what is the feasible/possible meaning of such definition for meta-arithmetic? Many thanks.

Feel free to add references if do you find it, to illustrate your explanation with examples or create an example with this purpose.

Answer 1

In general, see Metamathematics:

"the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories."

So, unless specified otherwise, it is the "logico-mathematical" study of arithmetic theory.

Some sources :

• Sthepen Cole Kleene, Introduction to Metamathematics (1952)

and:

• Petr Hájek & Pavel Pudlák, Metamathematics of first-order arithmetic (1993).