Generic filter for an atomless order is new

ID: generic-filter-for-an-atomless-order-is-new

If a generic filter for an atomless forcing order belonged to its ground model, then the complement would be a dense ground-model set. A condition outside is already there; a condition in has two incompatible strengthenings, at least one outside its directed filter. Genericity would then require meeting the complement, a contradiction.

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