It is an implementation of Peano arithmetic that Hofstadter uses to help explain Gödel's incompleteness theorems.
Like any system implementing the Peano axioms, TNT is capable of referring to itself (it is self-referential).
These are More variables can be constructed by adding the prime symbol after them; for example, In the more rigid version of TNT, known as "austere" TNT, only In Typographical Number Theory, the usual symbols of "+" for additions, and "·" for multiplications are used.
Any laxness would violate TNT's formation system (although it is trivially proved this formalism is unnecessary for operations which are both commutative and associative).
Note that unlike most other logical systems where quantifiers over sets require a mention of the element's existence in the set, this is not required in TNT because all numbers and terms are strictly natural numbers or logical boolean statements.