Faster access than browser!
67 relations: Abstract machine, Alan Turing, Algorithm, Algorithmic information theory, Axiom of choice, Axiomatic system, Berry paradox, Collatz conjecture, Complex plane, Computability theory, Computable function, Computational complexity theory, Computer program, Consistency, Continuum hypothesis, Countable set, Decidability (logic), Decision problem, Diophantine equation, Entscheidungsproblem, Fermat's Last Theorem, First-order logic, Formal language, Formal system, Gödel numbering, Gödel's incompleteness theorems, Goodstein's theorem, Gregory Chaitin, Group (mathematics), Group theory, Halting problem, Hilbert's tenth problem, Independence (mathematical logic), Integer, Iteration, John Horton Conway, Kolmogorov complexity, Kruskal's tree theorem, Liar paradox, Logic, Mathematical proof, Max Dehn, Natural number, Paris–Harrington theorem, Paul Cohen, Philosophy of mathematics, Polynomial, Proceedings of the USSR Academy of Sciences, Proof of impossibility, Ramsey theory, ..., Ramsey's theorem, Recursive set, Recursively enumerable set, Rice's theorem, Second-order arithmetic, Set theory, Soundness, String (computer science), Topology, Truth value, Turing machine, Uncountable set, Whitehead problem, Wicked problem, Word problem for groups, Yuri Matiyasevich, Zermelo–Fraenkel set theory. Expand index (17 more) »
Abstract machine
An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory.
New!!: Undecidable problem and Abstract machine · See more »
Alan Turing
Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.
New!!: Undecidable problem and Alan Turing · See more »
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
New!!: Undecidable problem and Algorithm · See more »
Algorithmic information theory
Algorithmic information theory is a subfield of information theory and computer science that concerns itself with the relationship between computation and information.
New!!: Undecidable problem and Algorithmic information theory · See more »
Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
New!!: Undecidable problem and Axiom of choice · See more »
Axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.
New!!: Undecidable problem and Axiomatic system · See more »
Berry paradox
The Berry paradox is a self-referential paradox arising from an expression like "The smallest positive integer not definable in under sixty letters" (note that this defining phrase has fifty-seven letters).
New!!: Undecidable problem and Berry paradox · See more »
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term.
New!!: Undecidable problem and Collatz conjecture · See more »
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
New!!: Undecidable problem and Complex plane · See more »
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.
New!!: Undecidable problem and Computability theory · See more »
Computable function
Computable functions are the basic objects of study in computability theory.
New!!: Undecidable problem and Computable function · See more »
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
New!!: Undecidable problem and Computational complexity theory · See more »
Computer program
A computer program is a collection of instructions for performing a specific task that is designed to solve a specific class of problems.
New!!: Undecidable problem and Computer program · See more »
Consistency
In classical deductive logic, a consistent theory is one that does not contain a contradiction.
New!!: Undecidable problem and Consistency · See more »
Continuum hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.
New!!: Undecidable problem and Continuum hypothesis · See more »
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.
New!!: Undecidable problem and Countable set · See more »
Decidability (logic)
In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a boolean true or false value that is correct (instead of looping indefinitely, crashing, returning "don't know" or returning a wrong answer).
New!!: Undecidable problem and Decidability (logic) · See more »
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.
New!!: Undecidable problem and Decision problem · See more »
Diophantine equation
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
New!!: Undecidable problem and Diophantine equation · See more »
Entscheidungsproblem
In mathematics and computer science, the Entscheidungsproblem (German for "decision problem") is a challenge posed by David Hilbert in 1928.
New!!: Undecidable problem and Entscheidungsproblem · See more »
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.
New!!: Undecidable problem and Fermat's Last Theorem · See more »
First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
New!!: Undecidable problem and First-order logic · See more »
Formal language
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.
New!!: Undecidable problem and Formal language · See more »
Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
New!!: Undecidable problem and Formal system · See more »
Gödel numbering
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number.
New!!: Undecidable problem and Gödel numbering · See more »
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
New!!: Undecidable problem and Gödel's incompleteness theorems · See more »
Goodstein's theorem
In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0.
New!!: Undecidable problem and Goodstein's theorem · See more »
Gregory Chaitin
Gregory John Chaitin (born 15 November 1947) is an Argentine-American mathematician and computer scientist.
New!!: Undecidable problem and Gregory Chaitin · See more »
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
New!!: Undecidable problem and Group (mathematics) · See more »
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
New!!: Undecidable problem and Group theory · See more »
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.
New!!: Undecidable problem and Halting problem · See more »
Hilbert's tenth problem
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900.
New!!: Undecidable problem and Hilbert's tenth problem · See more »
Independence (mathematical logic)
In mathematical logic, independence refers to the unprovability of a sentence from other sentences.
New!!: Undecidable problem and Independence (mathematical logic) · See more »
Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
New!!: Undecidable problem and Integer · See more »
Iteration
Iteration is the act of repeating a process, to generate a (possibly unbounded) sequence of outcomes, with the aim of approaching a desired goal, target or result.
New!!: Undecidable problem and Iteration · See more »
John Horton Conway
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
New!!: Undecidable problem and John Horton Conway · See more »
Kolmogorov complexity
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of the shortest computer program (in a predetermined programming language) that produces the object as output.
New!!: Undecidable problem and Kolmogorov complexity · See more »
Kruskal's tree theorem
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding.
New!!: Undecidable problem and Kruskal's tree theorem · See more »
Liar paradox
In philosophy and logic, the classical liar paradox or liar's paradox is the statement of a liar who states that he or she is lying: for instance, declaring that "I am lying" or "everything I say is false".
New!!: Undecidable problem and Liar paradox · See more »
Logic
Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.
New!!: Undecidable problem and Logic · See more »
Mathematical proof
In mathematics, a proof is an inferential argument for a mathematical statement.
New!!: Undecidable problem and Mathematical proof · See more »
Max Dehn
Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German-born American mathematician and student of David Hilbert.
New!!: Undecidable problem and Max Dehn · See more »
Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
New!!: Undecidable problem and Natural number · See more »
Paris–Harrington theorem
In mathematical logic, the Paris–Harrington theorem states that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, is true, but not provable in Peano arithmetic.
New!!: Undecidable problem and Paris–Harrington theorem · See more »
Paul Cohen
Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician.
New!!: Undecidable problem and Paul Cohen · See more »
Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives.
New!!: Undecidable problem and Philosophy of mathematics · See more »
Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
New!!: Undecidable problem and Polynomial · See more »
Proceedings of the USSR Academy of Sciences
The Proceedings of the USSR Academy of Sciences (Доклады Академии Наук СССР, Doklady Akademii Nauk SSSR (DAN SSSR), Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that was dedicated to publishing original, academic research papers in physics, mathematics, chemistry, geology, and biology.
New!!: Undecidable problem and Proceedings of the USSR Academy of Sciences · See more »
Proof of impossibility
A proof of impossibility, also known as negative proof, proof of an impossibility theorem, or negative result, is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general.
New!!: Undecidable problem and Proof of impossibility · See more »
Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear.
New!!: Undecidable problem and Ramsey theory · See more »
Ramsey's theorem
In combinatorial mathematics, Ramsey's theorem states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph.
New!!: Undecidable problem and Ramsey's theorem · See more »
Recursive set
In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which takes a number as input, terminates after a finite amount of time (possibly depending on the given number) and correctly decides whether the number belongs to the set.
New!!: Undecidable problem and Recursive set · See more »
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.
New!!: Undecidable problem and Recursively enumerable set · See more »
Rice's theorem
In computability theory, Rice's theorem states that all non-trivial, semantic properties of programs are undecidable.
New!!: Undecidable problem and Rice's theorem · See more »
Second-order arithmetic
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets.
New!!: Undecidable problem and Second-order arithmetic · See more »
Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
New!!: Undecidable problem and Set theory · See more »
Soundness
In mathematical logic, a logical system has the soundness property if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.
New!!: Undecidable problem and Soundness · See more »
String (computer science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.
New!!: Undecidable problem and String (computer science) · See more »
Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
New!!: Undecidable problem and Topology · See more »
Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.
New!!: Undecidable problem and Truth value · See more »
Turing machine
A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.
New!!: Undecidable problem and Turing machine · See more »
Uncountable set
In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.
New!!: Undecidable problem and Uncountable set · See more »
Whitehead problem
In group theory, a branch of abstract algebra, the Whitehead problem is the following question: Shelah (1974) proved that Whitehead's problem is undecidable within standard ZFC set theory.
New!!: Undecidable problem and Whitehead problem · See more »
Wicked problem
A wicked problem is a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognize.
New!!: Undecidable problem and Wicked problem · See more »
Word problem for groups
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element.
New!!: Undecidable problem and Word problem for groups · See more »
Yuri Matiyasevich
Yuri Vladimirovich Matiyasevich, (Ю́рий Влади́мирович Матиясе́вич; born March 2, 1947, in Leningrad) is a Russian mathematician and computer scientist.
New!!: Undecidable problem and Yuri Matiyasevich · See more »
Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
New!!: Undecidable problem and Zermelo–Fraenkel set theory · See more »
Redirects here:
Algorithmic insolubility, Algorithmically insoluble, Algorithmically unsolvable problem, Recursively undecidable, Semi-decidable, Uncomputable problem, Undecidable language, Undecidable set, Unsolvable problem.
References
[1] https://en.wikipedia.org/wiki/Undecidable_problem
