FOM: reply to Mr.Simpson's remark on AST

[Walter Felscher]

Mr. Simpson, in his note from November 27th, asked 
 
> Tell me, is it provable in AST that there exists a definable infinitesimal?

I do not think so, unless we restrict ourselves to a special "witnessed 
universe" in the sense of p.37 of Vopenka's book. - Also, Mr. Simpson wrote

> I have my doubts about whether AST provides a decent foundation for
> all of mathematics, as ZFC does.

Hm - 'all' of mathematics is difficult to judge. But as AST knows only of 
two infinite cardinalities (countability and uncountability), developments
requiring more than that will be lost.

W.F.