A note on $\mathbb{Z}$ as a direct summand of nonstandard models of weak systems of arithmetic

preprint2016arXivOpen access

There are nonstandard models of normal open induction ( $NOI$ ) for which $\mathbb{Z}$ is a direct summand of their additive group. We show that this is impossible for nonstandard models of $IE_2$ .

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A note on $\mathbb{Z}$ as a direct summand of nonstandard models of weak systems of arithmetic

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A note on Z\mathbb{Z}Z as a direct summand of nonstandard models of weak systems of arithmetic

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A note on $\mathbb{Z}$ as a direct summand of nonstandard models of weak systems of arithmetic