In many contexts we distinguish between proofs using AC and proofs which do not use AC. (To phrase this somewhat differently: If there is a proof without AC, this proof is usually preferred.)
I would like to know whether there are names commonly used for these two types of proofs.
In my mother tongue I have heard the names which could be translated to English as effective-proof (for the proof avoiding AC) and non-effective proof or ineffective proof (for the proofs employing AC).
When I searched for these term on internet 1, 2, 3 and in Google Books 1, 2, 3, I found some hits. But not enough to be persuaded that these two terms are widely used.
So I would like to ask
- Can some of the names for the proofs with/without AC which I mentioned above considered standard?
- Are other names for such proofs commonly used?