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 p1 ≤ p2 and q1 ≤ q2.
- 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 p ≤ q 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.
Read more about this topic: List Of Forcing Notions
Famous quotes containing the words product and/or forcing:
“The product of the artist has become less important than the fact of the artist. We wish to absorb this person. We wish to devour someone who has experienced the tragic. In our society this person is much more important than anything he might create.”
—David Mamet (b. 1947)
““Who cares what they say? It’s a nice way to live,
Just taking what Nature is willing to give,
Not forcing her hand with harrow and plow.””
—Robert Frost (1874–1963)