What is a Gödel numbering?
Q: What is a Gödel numbering?
A: A Gödel numbering is a function that assigns a unique natural number to each symbol and formula of a formal language, called a Gödel number (GN).
Q: Who first used the concept of Gödel numbering?
A: Kurt Gödel first used the concept of Gödel numbering for the proof of his incompleteness theorem.
Q: How can we interpret Gödel numbering?
A: We can interpret Gödel numbering as an encoding where each symbol of a mathematical notation is assigned a number, and a stream of natural numbers can represent some form or function.
Q: What do we call the natural numbers assigned by a Gödel numbering?
A: The natural numbers assigned by a Gödel numbering are called Gödel numbers or effective numbers.
Q: What does Rogers' equivalence theorem state?
A: Rogers' equivalence theorem states criteria for which those numberings of the set of computable functions are Gödel numberings.
Q: What is represented by a stream of Gödel numbers?
A: A numbering of the set of computable functions can be represented by a stream of Gödel numbers.
Q: Why is Gödel numbering important in formal number theory?
A: Gödel numbering is important in formal number theory as it provides a way to represent mathematical formulas and functions as natural numbers, which allows for the proof of important theorems like the incompleteness theorem.
