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Contrary statements about mathematics. (English) Zbl 1025.03053

From the text: The preceding paper, “Strong statements of analysis” by A. R. D. Mathias, defends a so-called full-blooded set theory without full detail [ibid. 32, No. 5, 513–526 (2000; Zbl 1025.03052)]. He again objects to a weak set theory which he calls ‘Mac’, in which the usual Zermelo-Fraenkel separation scheme is required only for formulas with suitably ‘restricted’ quantifiers. I had proposed that such separation is adequate for all standard uses of set theory in mathematics. But Mathias has not produced any counterexamples of actual mathematics which requires the use of a stronger separation.

MSC:

03E65 Other set-theoretic hypotheses and axioms
03E30 Axiomatics of classical set theory and its fragments
03G30 Categorical logic, topoi
18A15 Foundations, relations to logic and deductive systems
18B25 Topoi

Citations:

Zbl 1025.03052
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