Undecidable Statements

Some articles on undecidable statements, statements, undecidable, statement:

Bew - Examples of Undecidable Statements
... See also List of statements undecidable in ZFC There are two distinct senses of the word "undecidable" in mathematics and computer science ... in relation to computability theory and applies not to statements but to decision problems, which are countably infinite sets of questions each requiring a yes or no answer ... Such a problem is said to be undecidable if there is no computable function that correctly answers every question in the problem set (see undecidable problem) ...
Undecidable Problem - Examples of Undecidable Statements
... There are two distinct senses of the word "undecidable" in contemporary use ... in relation to Gödel's theorems, that of a statement being neither provable nor refutable in a specified deductive system ... second sense is used in relation to computability theory and applies not to statements but to decision problems, which are countably infinite sets of ...
Mathematical Proof - Undecidable Statements
... A statement that is neither provable nor disprovable from a set of axioms is called undecidable (from those axioms) ... Mathematicians have shown there are many statements that are neither provable nor disprovable in Zermelo-Fraenkel set theory with the axiom of choice (ZFC), the standard system of set theory in mathematics (assuming ... theorem shows that many axiom systems of mathematical interest will have undecidable statements ...

Famous quotes containing the word statements:

    A sentence is made up of words, a statement is made in words.... Statements are made, words or sentences are used.
    —J.L. (John Langshaw)