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Gerald Sacks
Gerald Enoch Sacks (1933 – October 4, 2019) was a logician whose most important contributions were in recursion theory. Named after him is Sacks forcing, a forcing notion based on perfect sets and the Sacks Density Theorem, which asserts that the partial order of the recursively enumerable Turing degrees is dense. Sacks had a joint appointment as a professor at the Massachusetts Institute of Technology and at Harvard University starting in 1972 and became emeritus at M.I.T. in 2006 and at Harvard in 2012. Sacks was born in Brooklyn in 1933. He earned his Ph.D. in 1961 from Cornell University 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, Sy Friedman, Leo Harrington, Richard Shore, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 main research interest lies in mathematical logic, in particular in set theory and recursion theory. Friedman is the brother of Ilene Friedman and the brother of mathematician Harvey Friedman. Biography He studied at Northwestern University and, from 1970, at the Massachusetts Institute of Technology. He received his Ph.D. in 1976 from MIT (his thesis ''Recursion on Inadmissible Ordinals'' was written under the supervision of Gerald E. Sacks). In 1979 Sy Friedman accepted a position at MIT, and in 1990 he became a full professor there. Since 1999 he has been a professor of mathematical logic at the University of Vienna (since 2018 retired). He is a Fellow of Collegium Invisibile. Selected publications and results He has authored ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Faculty
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 learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology School Of Science Faculty
Massachusetts (Massachusett language, Massachusett: ''Muhsachuweesut [Massachusett writing systems, məhswatʃəwiːsət],'' English: , ), officially the Commonwealth of Massachusetts, is the most populous U.S. state, state in the New England region of the Northeastern United States. It borders on the Atlantic Ocean and Gulf of Maine to the east, Connecticut and Rhode Island to the south, New Hampshire and Vermont to the north, and New York (state), New York to the west. The state's capital and List of municipalities in Massachusetts, most populous city, as well as its cultural and financial center, is Boston. Massachusetts is also home to the urban area, urban core of Greater Boston, the largest metropolitan area in New England and a region profoundly influential upon American History of the United States, history, academia, and the Economy of the United States, research economy. Originally dependent on agriculture, fishing, and trade. Massachusetts was transformed into a manuf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman empero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cornell University Alumni
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 and make contributions in all fields of knowledge—from the classics to the sciences, and from the theoretical to the applied. These ideals, unconventional for the time, are captured in Cornell's founding principle, a popular 1868 quotation from founder Ezra Cornell: "I would found an institution where any person can find instruction in any study." Cornell is ranked among the top global universities. The university is organized into seven undergraduate colleges and seven graduate divisions at its main Ithaca campus, with each college and division defining its specific admission standards and academic programs in near autonomy. The university also administers three satellite campuses, two in New York City and one in Education City, Qatar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Logicians
American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, people who self-identify their ancestry as "American" ** American English, the set of varieties of the English language native to the United States ** Native Americans in the United States, indigenous peoples of the United States * American, something of, from, or related to the Americas, also known as "America" ** Indigenous peoples of the Americas * American (word), for analysis and history of the meanings in various contexts Organizations * American Airlines, U.S.-based airline headquartered in Fort Worth, Texas * American Athletic Conference, an American college athletic conference * American Recordings (record label), a record label previously known as Def American * American University, in Washington, D.C. Sports teams Soccer * B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logicians
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kenneth Appel
Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana–Champaign, solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color. Biography Appel was born in Brooklyn, New York, on October 8, 1932. He grew up in Queens, New York, and was the son of a Jewish couple, Irwin Appel and Lillian Sender Appel. He worked as an actuary for a brief time and then served in the U.S. Army for two years at Fort Benning, Georgia, and in Baumholder, Germany. In 1959, he finished his doctoral program at the University of Michigan, and he also married Carole S. Stein in Philadelphia. The couple moved to Princeton, New Jersey, where Appel worked for the Institute for Defense Analyses from 1959 to 1961. His main work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, which conjectures that the partial order of the Turing degrees is logically equivalent to second-order arithmetic In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. A precur .... They showed that the Bi-interpretability Conjecture is equivalent to there being no nontrivial automorphism of the Turing degrees. They also exhibited limits on the possible automorphisms of the Turing degrees by showing that any automorphism will be arithmetically definable. References * External linkshome page * Living people American logicians 20th-century American ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steve Simpson (mathematician)
Stephen George Simpson is an American mathematician whose research concerns the foundations of mathematics, including work in mathematical logic, recursion theory, and Ramsey theory. He is known for his extensive development of the field of reverse mathematics founded by Harvey Friedman, in which the goal is to determine which axioms are needed to prove certain mathematical theorems. He has also argued for the benefits of finitistic mathematical systems, such as primitive recursive arithmetic, which do not include actual infinity. A conference in honor of Simpson's 70th birthday was organized in May 2016. Education Simpson graduated in 1966 from Lehigh University with a B.A. (summa cum laude) and M.A. in mathematics. He earned a Ph.D. from the Massachusetts Institute of Technology in 1971, with a dissertation entitled ''Admissible Ordinals and Recursion Theory'' and supervised by Gerald Sacks. Career After short-term positions at Yale University, the University of California, Be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
