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. [ edit ] Intuitions
Is there a way to determine how the average geodesic distance between nodes of a graph will change just by flipping (1) a single edge without having to traverse the whole graph like in the Djikstra algorithm? I'm currently doing this by expensively copying the graph, changing the edge, and then calculating the average geodesic distance of the new graph (using Dijkstra's algorithm) and subtracting it from the average geodesic distance of the original graph.. Is there a more clever way to to this?