FOM: infinitesimals and AST

[Walter Felscher]

Rick Sommer, on Nov. 11th, observed in connection with
infinitesimals, infeasible numbers etc. that

     To me the best explanation for these objects is through
     identifying infinite integers with something akin to the
     "infeasible numbers" that have been discussed in recent
     postings.  Roughly, the idea is to finitize the
     empirically relevant part of mathematical reality
     (including infinitesimal and infinite numbers).

It may be of interest to some readers of FOM that Petr
Vopenka during the 1970ies (partly in collaboration with
A.Sochor) developed a possibly related foundational program
which distinguished between standard and non-standard
objects (in particular: numbers) already in the setup of
its underlying 'alternative' set theory (AST), cf.
Vopenka's short book

    Mathematics in the Alternative Set Theory
    Leipzig, Teubner 1979 , 120 pp  .

W.F.