Contrary Statements About Mathematics

The preceding paper ‘Strong statements of analysis’by A. R. D. Mathias defends a so-called full-blooded set theorywithout full detail 3]. He again objects to a weak set theorywhich he calls ‘Mac’, in which the usual Zermelo–Fraenkelseparation scheme is required only for formulas with suitably‘restricted’ quantifiers. I had proposed that suchseparation is adequate for all standard uses of set theory inmathematics. But Mathias has not produced any counter examplesof actual mathematics which requires the use of a stronger separation.