incompleteness
21Gödel's incompleteness theorem — noun A theorem in mathematical logic that states that no consistent system can be used to prove its own consistency …
22gödel's incompleteness theorem — noun see gödel s theorem …
23Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …
24Undecidable problem — In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct an algorithm that leads to a yes or no answer the problem is not decidable.A decision problem is any …
25Rosser's trick — For the theorem about the sparseness of prime numbers, see Rosser s theorem. For a general introduction to the incompleteness theorems, see Gödel s incompleteness theorems. In mathematical logic, Rosser s trick is a method for proving Gödel s… …
26Gödel, Kurt — born April 28, 1906, Brünn, Austria Hungary died Jan. 14, 1978, Princeton, N.J., U.S. Austrian born U.S. mathematician and logician. He began his career on the faculty of the University of Vienna, where he produced his groundbreaking proof (see… …
27Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …
28Chaitin's constant — In the computer science subfield of algorithmic information theory, a Chaitin constant or halting probability is a real number that informally represents the probability that a randomly constructed program will halt. These numbers are formed from …
29Halting problem — In computability theory, the halting problem can be stated as follows: Given a description of a computer program, decide whether the program finishes running or continues to run forever. This is equivalent to the problem of deciding, given a… …
30George Boolos — Infobox Person name = George Boolos birth date = birth date|1940|9|4|mf=y birth place = New York, New York, U.S. death date = death date and age|1996|5|27|1940|9|4|mf=y death place = Cambridge, Massachusetts, U.S.George Stephen Boolos (September… …
