Gerald Enoch Sacks (1933 – October 4, 2019) was a

logician Logic is the study of correct reasoning. It includes both Mathematical logic, formal and informal logic. Formal logic is the science of Validity (logic), deductively valid inferences or of logical truths. It is a formal science investigating h ...

whose most important contributions were in

recursion theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has sinc ...

. Named after him is

Sacks forcing In mathematics, forcing is a method of constructing new models ''M'' 'G''of set theory by adding a generic subset ''G'' of a poset ''P'' to a model ''M''. The poset ''P'' used will determine what statements hold in the new universe (the 'extension') ...

, a

forcing Forcing may refer to: Mathematics and science * Forcing (mathematics), a technique for obtaining independence proofs for set theory *Forcing (recursion theory), a modification of Paul Cohen's original set theoretic technique of forcing to deal with ...

notion based on perfect sets and the Sacks Density Theorem, which asserts that the

partial order In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary ...

of the

recursively enumerable In computability theory, a set ''S'' of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable, provable or Turing-recognizable if: *There is an algorithm such that the ...

Turing degrees is dense. Sacks had a joint appointment as a professor at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...

and at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

starting in 1972 and became emeritus at M.I.T. in 2006 and at Harvard in 2012. Sacks was born in

Brooklyn Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York (state), New York. Kings County is the most populous Administrative divisions of New York (state)#County, county in the State of New York, ...

in 1933. He earned his Ph.D. in 1961 from

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to ...

under the direction of J. Barkley Rosser, with his dissertation ''On Suborderings of Degrees of Recursive Insolvability''. Among his notable students are Lenore Blum,

Harvey Friedman __NOTOC__ Harvey Friedman (born 23 September 1948)Handbook of Philosophical Logic, , p. 38 is an American mathematical logician at Ohio State University in Columbus, Ohio. He has worked on reverse mathematics, a project intended to derive the ax ...

, Sy Friedman, Leo Harrington, Richard Shore, Steve Simpson and Theodore Slaman.

Selected publications

Degrees of unsolvability
Princeton University Press 1963, 1966 * ''Saturated Model Theory'', Benjamin 1972

World Scientific 2010 * ''Higher Recursion theory'', Springer 1990 * ''Selected Logic Papers'', World Scientific 1999Review of ''Selected logic papers'' by Dag Normann, * ''Mathematical Logic in the 20th Century'', World Scientific 2003

References

Mathematical logicians American logicians Cornell University alumni 20th-century American mathematicians 21st-century American mathematicians Massachusetts Institute of Technology School of Science faculty Harvard University faculty 1933 births 2019 deaths {{US-mathematician-stub