TL;DR
This paper demonstrates that the induction-free theory PA^- is a sequential theory, contrasting it with Robinson's arithmetic, and explores its foundational properties in mathematical logic.
Contribution
It establishes that PA^- is sequential without relying on induction, providing new insights into the structure of axiomatized theories.
Findings
PA^- is a sequential theory without induction
Contrasts with Robinson's arithmetic in logical properties
Advances understanding of axiomatized theories' foundations
Abstract
We show that the universally axiomatized, induction-free theory PA^- is a sequential theory in the sense of Pudl\'ak [5], in contrast to the closely related Robinson's arithmetic.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.