 Let the generic multiverse 𝕍 be the result of closing V under generic extensions and generic refinements. One way to formalize this is by taking an external vantage point and start with a countable transitive model M. The generic multiverse based on M is then the smallest set  𝕍M such that  M ∈ 𝕍M and, for each pair of countable transitive models (N, N[G]) such that N ⊧ ZFC and G ⊆ ℙ is N-generic for some partial order in ℙ ∈ N, if either N or N[G] is in  𝕍M then both N and N[G] are in  𝕍M. 