thus was a goal for the Gödel machine to overcome. The Gödel machine has limitations of its own, however. According to Gödel's First Incompleteness Theorem...

incompleteness theorem Gödel, Escher, Bach Gödel machine Gödel's completeness theorem Gödel's speed-up theorem Löb's Theorem Minds, Machines and Gödel Non-standard...

Kurt Gödel. It's Not All In The Numbers: Gregory Chaitin Explains Gödel's Mathematical Complexities. Gödel photo gallery. (archived) Kurt Gödel MacTutor...

"Minds, Machines and Gödel" is J. R. Lucas's 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by...

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...

colony of ants. Gödel, Escher, Bach won the Pulitzer Prize for general non-fiction and the National Book Award for Science Hardcover. Gödel, Escher, Bach...

Chapter 5: "Gödel's completeness theorem". Stanford Encyclopedia of Philosophy: "Kurt Gödel"—by Juliette Kennedy. MacTutor biography: Kurt Gödel. Archived...

is seen in Kleene (1952) where Kleene shows how to write the Gödel number of a machine's "situation": he places the "m-configuration" symbol q4 over the...

constructible hierarchy L α {\displaystyle L_{\alpha }} . It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized...

indices in any other Gödel numbering. Optimal Gödel numberings are constructed by numbering the inputs of a universal Turing machine. A third notion of...