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29 relations: Alan Turing, Albert Muchnik, Annals of Mathematics, Bulletin of the American Mathematical Society, Computability theory, Computer science, Countable set, Decision problem, Dense order, Emil Leon Post, Equivalence class, Equivalence relation, Gerald Sacks, Halting problem, Join and meet, Lattice (order), Leo Harrington, Many-one reduction, Martin measure, Mathematical logic, Oracle machine, Partially ordered set, Recursively enumerable set, Robert I. Soare, Semilattice, Stephen Cole Kleene, Theodore Slaman, Turing jump, Turing reduction.
Alan Turing
Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.
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Albert Muchnik
Albert Abramovich Muchnik (born 1934) is a Russian mathematician who worked in the field of foundations and mathematical logic.
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Annals of Mathematics
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.
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Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.
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Computability theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Decision problem
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
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Dense order
In mathematics, a partial order or total order.
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Emil Leon Post
Emil Leon Post (February 11, 1897 – April 21, 1954) was an American mathematician and logician.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Gerald Sacks
Gerald Enoch Sacks (born 1933, Brooklyn) is a logician who holds a joint appointment at Harvard University as a professor of mathematical logic and the Massachusetts Institute of Technology as a professor emeritus.
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Halting problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.
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Join and meet
In a partially ordered set P, the join and meet of a subset S are respectively the supremum (least upper bound) of S, denoted ⋁S, and infimum (greatest lower bound) of S, denoted ⋀S.
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Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.
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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.
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Many-one reduction
In computability theory and computational complexity theory, a many-one reduction is a reduction which converts instances of one decision problem into instances of a second decision problem.
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Martin measure
In descriptive set theory, the Martin measure is a filter on the set of Turing degrees of sets of natural numbers, named after Donald A. Martin.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Oracle machine
In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems.
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Partially ordered set
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.
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Recursively enumerable set
In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if.
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Robert I. Soare
Robert Irving Soare is an American mathematician.
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Semilattice
In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset.
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Stephen Cole Kleene
Stephen Cole Kleene (January 5, 1909 – January 25, 1994) was an American mathematician.
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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.
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Turing jump
In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem a successively harder decision problem with the property that is not decidable by an oracle machine with an oracle for.
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Turing reduction
In computability theory, a Turing reduction from a problem A to a problem B, is a reduction which solves A, assuming the solution to B is already known (Rogers 1967, Soare 1987).
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Degree of unsolvability, Degrees of unsolvability, Post problem, Post's problem, Priority argument, Priority method, Recursively enumerable Turing degree, T degree, T-degree, Turing degrees, Turing equivalence (recursion theory).
References
[1] https://en.wikipedia.org/wiki/Turing_degree
