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Timeline for Is $S_R$ finitely generated?

Current License: CC BY-SA 4.0

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Jul 3, 2020 at 20:29 comment added YCor I added a full answer to the question.
Jul 1, 2020 at 18:20 history edited YCor CC BY-SA 4.0
added full answer
Jul 1, 2020 at 17:59 history edited YCor CC BY-SA 4.0
clarified what I'm answering
Jul 1, 2020 at 16:57 comment added markvs This answer does not answer the question.
Jul 1, 2020 at 12:32 vote accept Chain Markov
Jul 1, 2020 at 11:40 comment added YCor I even guess that there is no "computable surjective map $\mathbf{N}\to S_R$", that is, there is no computable map $g:\mathbf{N}^2\to\mathbf{N}$ such that $m\mapsto g(m,-)$ is a surjection from $\mathbf{N}$ to $S_R$. If so, it clearly follows that $S_R$ is not finitely generated.
Jul 1, 2020 at 11:15 history answered YCor CC BY-SA 4.0