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  1. Stuart T. Smith (1993). Quadratic Residues and $X^3+y^3=Z^3$ in Models of ${\Rm IE}1$ and ${\Rm IE}2$. Notre Dame Journal of Formal Logic 34 (3):420-438.
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  2. Stuart T. Smith (1992). Prime Numbers and Factorization in IE1 and Weaker Systems. Journal of Symbolic Logic 57 (3):1057 - 1085.
    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 (...)
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  3. Stuart T. Smith (1992). Prime Numbers and Factorization in $Mathrm{IE}_1$ and Weaker Systems. Journal of Symbolic Logic 57 (3):1057-1085.
    We show that $\mathrm{IE}_1$ 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 Bezout 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 $\hat\mathbb{Z} = \Pi_p\mathbb{Z}_p$, the product of the $p$-adic integers for (...)
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  4. Stuart T. Smith (1989). Nonstandard Definability. Annals of Pure and Applied Logic 42 (1):21-43.
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  5. Stuart T. Smith (1987). Nonstandard Characterizations of Recursive Saturation and Resplendency. Journal of Symbolic Logic 52 (3):842-863.
    We prove results about nonstandard formulas in models of Peano arithmetic which complement those of Kotlarski, Krajewski, and Lachlan in [KKL] and [L]. This enables us to characterize both recursive saturation and resplendency in terms of statements about nonstandard sentences. Specifically, a model M of PA is recursively saturated iff M is nonstandard and M-logic is consistent.M is resplendent iff M is nonstandard, M-logic is consistent, and every sentence φ which is consistent in M-logic is contained in a full satisfaction (...)
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