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Mar 7 at 2:35 history became hot network question
Mar 6 at 19:52 answer added Theodore Slaman timeline score: 10
Mar 6 at 19:03 history edited Noah Schweber
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Mar 6 at 19:01 comment added Noah Schweber @CommandMaster There are indeed maximal Turing-independent sets, but they don't satisfy the property the OP's after. See my answer.
Mar 6 at 19:00 comment added Daniel Weber Oh, right. However, I think you can use the same argument with Zorn's lemma which shows the existence of a basis to prove the existence of a maximum Turing independent set
Mar 6 at 18:56 comment added Noah Schweber @CommandMaster that might not be Turing independent, e.g. our Hamel basis could have elements satisfying $x=\pi y$.
Mar 6 at 18:56 comment added Daniel Weber Couldn't you just take a Hamel basis of the reals?
Mar 6 at 18:40 answer added Noah Schweber timeline score: 11
S Mar 6 at 18:34 review First questions
Mar 6 at 19:36
S Mar 6 at 18:34 history asked Fiona CC BY-SA 4.0