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

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

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 since e ...

. Named after him is Sacks forcing, a forcing notion based on

perfect set In general topology, a subset of a topological space is perfect if it is closed and has no isolated points. Equivalently: the set S is perfect if S=S', where S' denotes the set of all Limit point, limit points of S, also known as the derived set ...

s 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 degree In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set. Overview The concept of Turing degree is fund ...

s is

dense Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...

. Sacks had a joint appointment as a professor at the

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

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 higher le ...

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. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, be ...

in 1933. He earned his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

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 teach an ...

under the direction of

J. Barkley Rosser John Barkley Rosser Sr. (December 6, 1907 – September 5, 1989) was an American logician, a student of Alonzo Church, and known for his part in the Church–Rosser theorem, in lambda calculus. He also developed what is now called the "Rosser siev ...

, with his dissertation ''On Suborderings of Degrees of Recursive Insolvability''. Among his notable students are

Lenore Blum Lenore Carol Blum (née Epstein, born December 18, 1942) is an American computer scientist and mathematician who has made pioneering contributions to the theories of real number computation, cryptography, and pseudorandom number generation. She ...

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 axi ...

Sy Friedman Sy-David Friedman (born May 23, 1953 in Chicago) is an American and Austrian mathematician and a (retired) professor of mathematics at the University of Vienna and the former director of the Kurt Gödel Research Center for Mathematical Logic. His ...

Leo Harrington Leo Anthony Harrington (born May 17, 1946) is a professor of mathematics at the University of California, Berkeley who works in recursion theory, model theory, and set theory. Having retired from being a Mathematician, Professor Leo Harrington is ...

Richard Shore Richard Arnold Shore (born August 18, 1946) is a professor of mathematics at Cornell University who works in recursion theory. He is particularly known for his work on \mathcal, the partial order of the Turing degrees. * Shore settled the Hartl ...

, Steve Simpson and

Theodore Slaman Theodore Allen Slaman (born April 17, 1954) is a professor of mathematics at the University of California, Berkeley who works in recursion theory. Slaman and W. Hugh Woodin formulated the Bi-interpretability Conjecture for the Turing degrees, wh ...

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