Prime numbers and factorization in IE1 and weaker systems

Journal of Symbolic Logic 57 (3):1057 - 1085 (1992)
We show that IE1 proves that every element greater than 1 has a unique factorization into prime powers, although we have no way of recovering the exponents from the prime powers which appear. The situation is radically different in Bézout models of open induction. To facilitate the construction of counterexamples, we describe a method of changing irreducibles into powers of irreducibles, and we define the notion of a frugal homomorphism into Ẑ = ΠpZp, the product of the p-adic integers for each prime p
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DOI 10.2307/2275449
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Primes and Their Residue Rings in Models of Open Induction.Angus Macintyre & David Marker - 1989 - Annals of Pure and Applied Logic 43 (1):57-77.

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