0

Arithmetic is the core of the study of numbers; from natural numbers you can construct the other numbers. Now, I have heard that set theory is the most fundamental core of mathematics; for this reason the following question arose in me:

can Peano axioms be proven in set theory?

J. W. Tanner
  • 60,406
Rata mágica
  • 369
  • 3
    Yes, we can. See e.g. Enderton – Mauro ALLEGRANZA Oct 26 '21 at 13:49
  • 1
    See also this post – Mauro ALLEGRANZA Oct 26 '21 at 13:51
  • I wouldn't think of set theory as "the most fundamental". A theory like $\mathsf{ZFC}$ could function as a foundation for mathematics, since 99% of the theorems proved in other fields of mathematics can be derived from $\mathsf{ZFC}$. However, alternative foundational systems of mathematics exist, most notably category theory. There is no reason to think that set theory is more fundamental than category theory, or the other way around. Moreover, while Peano arithmetic is almost universally accepted as "true", certain parts of $\mathsf{ZFC}$ and of category theory remain controversial. – Vsotvep Oct 26 '21 at 14:57

0 Answers0