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We survey some lesser-known facts concerning properties of embeddings and projections between forcing notions. We will also state some generalizations of Easton’s lemma. To our knowledge, many of these facts have not b...

Suppose M and N are transitive models of set theory, P is a forcing notion in M and G is P-generic over M. An elementary embedding j : (M, ∈) → (N, ∈) lifts to M[G] if there is j+ : (M[G], G, ∈) → (N[j+(G)], j+...