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Construction of the class FN. (English) Zbl 0611.03025

In the paper (whose author is still a student) it is proved that the class FN (of finite natural numbers) is definable by a normal formula from a well ordering of the universal class V. This fact implies the assertion that in a modified AST (Morse’s scheme substituted by Gödel’s scheme) the axiom of choice in the form ”there is a well ordering of V” is stronger than in the form using the existence of an extensional coding. The assertion is given here without any proof or quotation (I also have not found any quotation, although the model demonstrating it is well known in the Prague AST seminar). Let us note (although without any proof or quotation) that the existence of a countable class suffices for proving the equivalence of the mentioned two forms of the axiom of choice in the modified AST.
Reviewer: K.Čuda

MSC:

03E70 Nonclassical and second-order set theories
03H99 Nonstandard models
03E25 Axiom of choice and related propositions