Re: Cauchy completeness of Cauchy reals

[Dusko Pavlovic <dusko@kestrel.edu>]

Martin Escardo wrote:

>NB. Freyd characterized the Dedekind reals as a final coalgebra. Alex
>Simpson and I characterized "the Cauchy completion of the rationals
>within the Dedekind reals" as a free algebra
>
and vaughan pratt and i characterized the cauchy reals as a final
coalgebra. the papers are i proceedings of CMCS 99 and in TCS 280. in
fact, freyd came up with his characterization of the closed interval
while commenting on our first paper, where vaughan and i worked with the
semiopen interval.

but it is fair to say that the algebraic approach allows easier
algebraic operations on reals. (i only managed to multiply them in one
of our coalgebras, and in a very inefficient way.)

-- dusko

BTW have you seen the book:

    Life Itself. A Comprehensive Inquiry Into the Nature, Origin, and
Fabrication of Life
    by Robert Rosen (Columbia University Press 1991)

it was referenced in a biology paper, i found it in the biology library,
and it's full of categories. (yes, i kno, people often do that to sound
complicated, but this seems like honest work, perhaps even inspiring,
although it does not go very deep.)