[FOM] V = L mathematically
Harvey Friedman
friedman at math.ohio-state.edu
Sun Feb 12 23:59:55 EST 2006
We look at order invariant relations R containedin alpha^k x alpha^k =
alpha^2k, in the usual sense. We say that R is strictly dominating iff
R(x,y) implies max(x) < max(y).
We write R# for the unique A containedin alpha^k such that
R[A] = alpha^k \ A.
THEOREM. In a weak fragment of ZF, we can prove V = L if and only if
every set of ordinals is a cross section of some R#
where R is a strictly dominating order invariant relation contained in some
alpha^k x alpha^k = alpha^2k. (Cross section obtained by fixing the first
k-1 arguments).
We can also use this as a definition of the
**constructible multivariate relations on the ordinals**
as the multivariate cross sections of the R#.
The constructible sets are then defined as the sets A such that
(TC(A),epsilon) is isomorphic to some (alpha,S), where S is a constructible
binary relation on alpha.
Harvey Friedman
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