Forcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique invented by Paul Cohen for proving consistency and independence results. It was first used, in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory. Forcing was considerably reworked and simplified in the 1960s, and has proven to be an extremely powerful technique both within set theory and in areas of mathematical logic such as recursion theory.
Descriptive set theory uses both the notion of forcing from recursion theory as well as set theoretic forcing. Forcing has also been used in model theory but it is common in model theory to define genericity directly without mention of forcing.
Read more about Forcing (mathematics): Intuitions, Forcing Posets, Countable Transitive Models and Generic Filters, Forcing, Consistency, Cohen Forcing, The Countable Chain Condition, Easton Forcing, Random Reals, Boolean-valued Models, Meta-mathematical Explanation, Logical Explanation
Famous quotes containing the word forcing:
“An empty head is not really empty; it is stuffed with rubbish. Hence the difficulty of forcing anything into an empty head.”
—Eric Hoffer (1902–1983)