Is anyone aware of alternative axioms to induction? To be precise, consider peano axioms without induction PA-. Is there any axiom/axiom schema that is equiconsistent to induction, assuming PA-? If so, why does it appear that nobody investigating it?

To contextualize this question, I refer to discovery of the equiconsistency of the non-Euclidean geometries. The geometry has flourished (or at least, developed) to its modern state with manifold theories and later developments was only possible with the recognition of non-Euclidean geometries. For a long time, Euclidean geometry and the Parallel Postulate was seen as the only geometry, very much as today's standard model for number theory ${\mathbb N}$ and the induction axiom is seen as the only number theory. (at least to the extent that i'm aware of, so that's why I'm asking this question.) I wonder why, therefore, that there is only one number theory, and no alternatives like non-Induction number theory.

Note: I am aware that recursion theorists study fragments of induction. However, in the sense of which I'm asking, this does not count at alternative axioms to induction since ${\mathbb N}$ is still a model of these these fragments. Using my geometry analogy, these fragments amount to saying that the Parallel Postulate does not hold everywhere throughout space, something like space is not homogeneous but still has some symmetry.