A Gödel numbering is any way of assigning numbers to the formulas of a language. This is often useful in allowing sentences of a language to be self-referential. The number associated with a formula is called its Gödel number and is denoted .
More formally, if is a language and is a surjective partial function from the terms of to the formulas over then is a Gödel numbering. may be any term such that . Note that is not defined within (there is no formula or object of representing ), however properties of it (such as being in the domain of , being a subformula, and so on) are.
Athough anything meeting the properties above is a Gödel numbering, depending on the specific language and usage, any of the following properties may also be desired (and can often be found if more effort is put into the numbering):
If is a subformula of then
For every number , there is some such that
|Date of creation||2013-03-22 12:58:21|
|Last modified on||2013-03-22 12:58:21|
|Last modified by||Henry (455)|