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Have you ever heard of this result?

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  • David Hobby
    Hi. We stumbled across the following results, and wonder if anyone has already found them. They certainly feel like things that could have been done 50 to 100
    Message 1 of 1 , Aug 16, 2007
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      Hi. We stumbled across the following results,
      and wonder if anyone has already found them.
      They certainly feel like things that could
      have been done 50 to 100 years ago.

      Consider groupoids, and look at "generalized
      associative laws". These would be identities
      similar to ((uv)w)((xy)z) = ((((uv)w)x)y)z.
      (I'm using concatenation for the groupoid
      operation.) Specifically, a generalized
      associative law is an identity between two
      terms, where the same variables each appear
      once, in the same order, and the terms are
      only distinguished by how they are parenthesized.

      The result is that the following two element
      groupoids satisfy no generalized associative
      laws. The groupoid on {0,1} where the operation
      is implication. (That is, 00 = 01 = 11 = 1, and
      10 = 0.) And the groupoid on {0,1} where the
      operation is NAND. (00 = 01 = 10 = 1, and 11 = 0).

      Help?

      ---David
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