Universally Baire Book Updates
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Solovay proved that the reals that are Delta^1_2
in a countable ordinal are the same as the reals in L.
We prove this assuming omega_1 is inaccessible in L,
but this is not needed.
While having omega_1 be inaccessible in L allows us to
take the mutual generics to be in V,
the mutual generics can actually be taken to be in an outer model of V
which allows for the optimal result.