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nLab > Latest Changes: Boone conjecture

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  1. The conjecture is not true for all single-sorted algebraic theories and this was known by Soviet mathematicians. I added a short high-level explanation on this and some references to translated works that have more detail. Presumably one should edit rest of the page (and references to it) to make it clear throughout that (i) the conjecture is false (ii) the general question “Which algebraic categories have the Higman property?” is still interesting (and potentially something category-theorists could study).

    diff, v6, current

    • CommentRowNumber2.
    • CommentAuthorRichard Williamson
    • CommentTimeDec 22nd 2020
    • (edited Dec 22nd 2020)

    Thank you for this, great to bring this work to people’s attention. Yes, I agree, the Idea section should be tweaked in the way you mention. I don’t know anything about this, so will refrain from making the edits myself; perhaps you would like to do so?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 23rd 2020
    • (edited Dec 23rd 2020)

    I have just added the respective lines from #1 to the Idea section:

    While in fact the conjecture is not true for all single-sorted algebraic theories (see below), as was known by Soviet mathematicians, the general question “Which algebraic categories have the Higman property?” is still interesting (and potentially something category-theorists could study).

    diff, v8, current

  4. I added more or less the same sentence to the two other pages pointing to this page - namely Lawvere theory and Higman's embedding theorem.

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