> some minimally Turing-complete subset of the language How about integer arithmetic? That's the programming language Goedel used for his incompleteness theore

> some minimally Turing-complete subset of the language How about integer arithmetic? That's the programming language Goedel used for his incompleteness theorems (specifically, he showed that the semantics of any formal logical system can be implemented in Peano arithmetic, using Goedel numbering as an example). I wouldn't call that a useful definition though. There are reasons why we don't treat RAM as one giant binary integer.