The mapping between arithmetical expressions and meta-arithmetical sta
tements, based on Godel's numbering, cannot go awry in any ''non-stand
ard'' model, as Sloman suggested. Godel's numbering itself cannot go a
wry, because it involves only the standard model, and the extra elemen
ts in ''non-standard'' models, in so far as they are involved in meta-
theoretical interpretation at all, cannot affect the mapping, because
they have no independent meta-theoretical meaning. (C) 1998 Elsevier S
cience B.V.