Finite and infinite primes in models of PA
Daniele Mundici
TL;DR
This paper characterizes models of Peano arithmetic that contain infinitely many infinite primes with the property that adding 2 yields a number with no finite prime divisor.
Contribution
It introduces a novel characterization of models of PA involving infinite primes and their properties related to finite prime divisors.
Findings
Models of PA with infinitely many infinite primes exist.
Infinite primes in these models have specific properties regarding finite primes.
The paper provides a new perspective on prime elements in non-standard models.
Abstract
We characterize models of Peano arithmetic (PA) with infinitely many infinite primes p such that p + 2 has no finite prime divisor.
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.
Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical and Theoretical Analysis · Rings, Modules, and Algebras