Re: to PTJ

[Ronnie Brown <ronnie.profbrown@btinternet.com>]

I am curious to know how all this fits with partial algebraic 
operations. The axioms for a groupoid allow for the empty groupoid. That 
reminds me that Philip Higgins wrote about partial algebraic structures in

@article {Higgins-algebrawithoperators,
    AUTHOR = {Higgins, Philip J.},
     TITLE = {Algebras with a scheme of operators},
   JOURNAL = {Math. Nachr.},
  FJOURNAL = {Mathematische Nachrichten},
    VOLUME = {27},
      YEAR = {1963},
     PAGES = {115--132},
      ISSN = {0025-584X},
   MRCLASS = {18.10},
  MRNUMBER = {MR0163940 (29 \#1239)},
MRREVIEWER = {A. Heller},
}

and he told me that years later he got a paper from a computer scientist 
saying `Higgins' theorem is true as stated' , which apparently concerned 
the empty structure!

Does anyone on this list know a reference for axioms for group theory 
which are related to Dakin's axioms for a simplicial T-complex;
1) degenerate implies thin;
2) every horn has a unique thin filler;
3) if all faces but one of a thin element are thin, then so also is the 
remaining face.

The last axiom is related to associativity. I am sure I had a reference 
at one time, but have lost it.

Ronnie Brown

burroni@math.jussieu.fr wrote:
> Hi,
> You can find this equation (and ref to Higman and Neumann) in the GTM 
> springer no 26 page 7 : E.G. manes "Algebraic Theory.
>      xxxdydzdxxdxdzddd=y
> (polish notations and d is the binary operation.)
>
> Best,
> Albert
>

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