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...

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...

nor disproved from the axioms. To prove this, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers...

his Gödel, Escher, Bach: The Gödel number of a formula is obtained by concatenating the Gödel numbers of each symbol making up the formula. The Gödel numbers...

be given a standard Gödel numbering by the natural numbers. If Φ {\displaystyle \Phi } is the formula with the smallest Gödel number that can be used to...

language of arithmetic is assigned a distinct number. This procedure is known variously as Gödel numbering, coding and, more generally, as arithmetization...

mathematics, a Gödel numbering for sequences provides an effective way to represent each finite sequence of natural numbers as a single natural number. While...

Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development...

order-indiscernibles in the Gödel constructible universe. It is often encoded as a subset of the natural numbers (using Gödel numbering), or as a subset of the...

dense Gödel numbering of syntactically correct Brainfuck programs. A dense Gödel numbering is called optimal if, for any other Gödel numbering α {\displaystyle...

admissible numbering in the literature. Complete numbering Cylindrification Gödel numbering Description number "Computability Theory - an overview | ScienceDirect...

philosopher Kurt Gödel postulated in 1947. The loophole would permit the American democracy to be legally turned into a dictatorship. Gödel told his friend...

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

or stacks can be handled by interpreting the number in a cell in specific ways, that is, by Gödel numbering the possible structures. Control flow constructs...

complex values is formalized as the set of numbers that, via a specific Gödel numbering, correspond to inputs that satisfy the decision problem's criteria...

in the paper. In order to prove these results, Gödel introduced a method now known as Gödel numbering. In this method, each sentence and formal proof...

{\displaystyle f} is computable (which is ultimately an assumption about the Gödel numbering scheme), so there is a formula G f ( x , y ) {\displaystyle {\mathcal...

 5). Gödel's axiom B7 (Gödel 1940, p. 5). Gödel's axiom B8 (Gödel 1940, p. 5). Gödel 1940, p. 6; Kanamori 2012, p. 70. Kanamori 2009, p. 57; Gödel 2003...

is consistent). That CH is consistent with ZFC was demonstrated by Kurt Gödel in 1940, when he showed that its negation is not a theorem of ZFC. That...

idea was to map mathematical notation to a natural number (using a Gödel numbering). There are codes using colors, like traffic lights, the color code...

computable. Any productive set is not computably enumerable. Given a Gödel numbering ϕ {\displaystyle \phi } of the computable functions, the set { ⟨ i...

Gödel's incompleteness theorems, which were published in 1931, establish that there is a formal statement (one for each appropriate Gödel numbering scheme)...

parallelism Galois group Fundamental theorem of Galois theory (to do) Gödel number Gödel's incompleteness theorem Group (mathematics) Halting problem insolubility...

theorem. Roger's equivalence theorem provides a characterization of the Gödel numbering of the computable functions in terms of the smn theorem and the UTM...

formal languages. Using an encoding such as Gödel numbering, any string can be encoded as a natural number, via which a decision problem can be defined...

influenced by Kurt Gödel's earlier work on his incompleteness theorem, especially by the method of assigning numbers (a Gödel numbering) to logical formulas...

axiom. In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new light on the problem. Some feel that Gödel's theorems give a negative...

computable subset of a formal language. The set of Gödel numbers of arithmetic proofs described in Kurt Gödel's paper "On formally undecidable propositions of...

constructing a Gödel numbering for lambda expressions, he constructs a lambda expression e that closely follows the proof of Gödel's first incompleteness...

of this 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...