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.