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Prime numbers and factorization in IE1 and weaker systems

Published online by Cambridge University Press:  12 March 2014

Stuart T. Smith
Stuart T. Smith*
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel, E-mail: mtshamsh@weizmann.bitnet
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Abstract

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 , the product of the p-adic integers for each prime p.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 3 , September 1992 , pp. 1057 - 1085
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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