## Q-Naturals: A Counter-Example to Tennenbaum's Theorem

**Authors:** Wes Hansen

In what follows we develop foundations for a set of non-standard natural numbers we call q-naturals, where q stands for quanta, by the recursive generation of reflexive sets. From the practical perspective, these q-naturals correspond to ordered pairs of natural numbers with the lexicographic ordering, hence, they are isomorphic to ω^2. In addition, we demonstrate a novel definition of the arithmetical operation, multiplication, which turns out to be recursive. This, in turn, enables our demonstration of a counter-example to Tennenbaum’s Theorem.

**Comments:** 9 Pages.

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### Submission history

[v1] 2017-03-25 15:57:12

[v2] 2017-03-27 15:53:09

[v3] 2017-03-29 16:58:21

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