What's meta-arithmetic? 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.

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 :


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*Sthepen Cole Kleene, Introduction to Metamathematics (1952)


and:


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

