FOM: Re: Axiom of constructibility

Harvey Friedman friedman at
Sun Feb 13 20:31:45 EST 2000

Reply to Kanovei Sun, 13 Feb 00 18:49.

>Still there is an interesting fom-like question related
>to V=L:
>QUESTION: is there any mathematically meaningful statement
>about projective sets
>(in particular different from consistency of something)
>which V=L does not decide ?

A major research effort of mine from the mid 70's through the mid 80's was
to give mathematically meaningful statements about Borel sets that require
large cardinals to prove and are absolute. In particular, they are
independent of ZFC + V=L.

H. Friedman, On the Necessary Use of Abstract set Theory, Advances in
Math., VOl. 41, No. 3, (September 1981), pp. 209-280.

L.J. Stanley, Borel Diagonalization and Abstract Set Theory: Recent
Results, in: Harvey Friedman's Research on the Foundations of Mathematics,
Studies in Logic and the Foundations of Mathematics, Volume 117, ed. L.A.
Harrington, M.D. Morley, A. Scedrov and S.G. Simpson, North-Holland, 1985,
pp. 11-86.

These days, I have progressed (regressed) into the integers.

Of course, I could go back to this project and do much better, as I am now
older, smarter, and wiser. And I might just do that.

More information about the FOM mailing list