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

Walter Felscher walter.felscher at
Fri Nov 28 11:15:07 EST 1997

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.


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