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Jul 28, 2019 at 13:08 comment added Robert Furber @YCor Yes, exactly, and I've changed the answer to clarify that I always mean a finite presentation. It is even possible to produce such a presentation explicitly, by writing a kind of compiler from Turing machines to finite presentations.
Jul 28, 2019 at 13:06 history edited Robert Furber CC BY-SA 4.0
Clarified that I mean finite presentations.
Jul 28, 2019 at 6:58 comment added YCor In your part on logical decidability, do you mean there is a (finite??) presentation $M$ such that, assuming that ZFC is consistent, then both (ZFC and $M$ is a presentation of the trivial group) and (ZFC and $M$ is a presentation of a nontrivial group) are consistent?
Jul 28, 2019 at 3:10 history answered Robert Furber CC BY-SA 4.0