Paul J. Cohen (1934-2007) was an American mathematician who received the Fields medal in 1966 for his groundbreaking work in set theory.
In his proof of the independence of the continuum hypothesis from the ZFC axioms of set theory he introduced forcing into the arsenal of mathematical logic and model theory:
It was in 1963 that we were hit by a real bomb, however, when Paul J. Cohen discovered his method of ‘forcing’… Set theory could never be the same after Cohen, and there is simply no comparison whatsoever in the sophistication of our knowledge about models for set theory today as contrasted to the pre-Cohen area. One of the most striking consequences of his work is the realization of the extreme relativity of the notion of cardinal number. Dana Scott in (Bell 2005, p.xiv)
From a broader perspective Cohen’s results fit nicely into the landscape of relativising set theory and the rise of ‘variable sets’in the work of Grothendieck, Lawvere and Tierney on topos theory in the 60s and afterwards.
Introducing forcing in set theory as a way to prove the independence of the continuum hypothesis from ZFC:
Paul J. Cohen: The independence of the Continuum Hypothesis, PNAS 50 6 (1963) 1143-1148 [doi:10.1073/pnas.50.6.1143, pdf]
Paul J. Cohen: The independence of the Continuum Hypothesis II, PNAS 51 1 (1963) 105-110 [doi:10.1073/pnas.51.1.105, pdf]
Paul J. Cohen: Set theory and the continuum hypothesis, Benjamin, New York (1966) [ark:/13960/s2qndx0d4n7]
Historical reminiscences:
J. L. Bell, Set Theory - Boolean-Valued Models and Independence Proofs , Oxford Logic Guides 47 3rd ed. Oxford UP 2005.
A. Church, Paul J. Cohen and the Continuum Problem, pp.15-20 in Proceedings ICM Moscow 1966. (pdf)
Last revised on December 25, 2024 at 18:45:07. See the history of this page for a list of all contributions to it.