Initial function of recursion theory

The initial functions are the zero function, the successor function, and all coordinate projections.

Table of contents

Zero function ( $Z$ )

The zero function has the constant value

Z (x) = 0.

Dummy variables give a zero function of any finite arity.

Successor function ( $S$ )

The successor function is

S (n) = n + 1.

Projection function ( $π_{i}^{k}$ )

The

i

th

k

-ary projection returns its

i

th input:

π_{i}^{k} (x_{1}, \dots, x_{k}) = x_{i} .

 Ancestors (6)

 Incoming links (2)

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 120 / 4 / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 12F / i / Solution

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codex/initial-functions-of-recursion-theory

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