Q:Information: - In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The "transfinite" cardinal numbers describe the sizes of infinite sets. - In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies. - The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group beyond the sports context. The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University. The term "Ivy League" has connotations of academic excellence, selectivity in admissions, and social elitism. - Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - Dana Stewart Scott (born October 11, 1932) is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, California. His research career involved computer science, mathematics, and philosophy. His work on automata theory earned him the ACM Turing Award in 1976, while his collaborative work with Christopher Strachey in the 1970s laid the foundations of modern approaches to the semantics of programming languages. He has worked also on modal logic, topology, and category theory. - Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those. - In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least such that =). The proposition that such cardinals exist cannot be proved in the most common axiomatization of set theory, namely ZFC, and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results. In other words, they can be seen, in Dana Scott's phrase, as quantifying the fact "that if you want more you have to assume more". - In set theory, a Woodin cardinal (named for W. Hugh Woodin) is a cardinal number such that for all functions - Harvard University is a private Ivy League research university in Cambridge, Massachusetts, established in 1636, whose history, influence, and wealth have made it one of the world's most prestigious universities. - A research university is a university that expects all its tenured and tenure-track faculty to continuously engage in research, as opposed to merely requiring it as a condition of an initial appointment or tenure. Such universities can be recognized by their strong focus on innovative research and the prestige of their brand names. On the one hand, research universities strive to recruit faculty who are the most brilliant minds in their disciplines in the world, and their students enjoy the opportunity to learn from such experts. On the other hand, new students are often disappointed to realize their undergraduate courses at research universities are overly academic and fail to provide vocational training with immediate "real world" applications; but many employers value degrees from research universities because they know that such coursework develops fundamental skills like critical thinking. - In mathematical logic, suppose "T" is a theory in the language - William Hugh Woodin ( born April 23 , 1955 ) is an American mathematician and set theorist at Harvard University . He has made many notable contributions to the theory of inner models and determinacy . A type of large cardinal , the Woodin cardinal , bears his name . After reading the paragraphs above, we are interested in knowing the entity with which 'w. hugh woodin' exhibits the relationship of 'field of work'. Find the answer from the choices below. Choices: - computer science - education - history - language - mathematical logic - mathematician - mathematics - philosophy - research - science - set theory - track - training
A:
set theory