[visualstudio]

Not a mathematician. If the goal is simplicity why can't you use Peano's axioms?

[Retra]

The Peano axioms don't do very much, they just help model the natural numbers. You still need something to model the logic and provide foundations more complex subjects like analysis.

[Koshkin]

> simplicity

It might be possible to build a set theory and the rest of mathematics based on the integers, but I am sure the result wouldn't look simple.