FOM: Re: V=L

Karlis Podnieks podnieks at
Fri Apr 24 02:36:08 EDT 1998

Once again about putting the statement "All sets can be built by
using comprehension axioms of ZF" into one formula.

Goedel introduced a fixed set of 7 (or so) operations, defined
the class L of all "constructible" sets, and proved that all
comprehension axioms hold on L. Let us generalize this approach
by defining L(S) for any finite set S of (absolute?) operations.
I would conjecture that if all comprehension axioms hold on
L(S), then L(S)=L.

If this would be true, for me, it would justify adopting of V=L
instead of the regularity axiom to obtain a "better" set theory
than ZFC. May I ask the opinion of professionals?

Best wishes, K.Podnieks, podnieks at
University of Latvia, Institute of Mathematics and Computer

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