List of Forcing Notions - Product Forcing

Product Forcing

Taking a product of forcing conditions is a way of simultaneously forcing all the conditions.

  • Finite products: If P and Q are posets, the product poset P× Q has the partial order defined by (p1, q1) ≤ (p2, q2) if p1p2 and q1q2.
  • Infinite products: The product of a set of posets Pi, i I, each with a largest element 1 is the set of functions p on I with p(i) P(i) and such that p(i) = 1 for all but a finite number of i. The order is given by pq if p(i) ≤ q(i) for all i.
  • The Easton product (after William Bigelow Easton) of a set of posets Pi, i I, where I is a set of cardinals is the set of functions p on I with p(i) P(i) and such that for every regular cardinal γ the number of elements α of γ with p(α) ≠ 1 is less than γ.

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