Number Theory


The Q-Universe: A Set Theoretic Construction

Authors: Wes Hansen

In an earlier paper, “Q-Naturals: A Counter-Example to Tennenbaum’s Theorem,” we developed a set of non-standard naturals called q-naturals and demonstrated a counter-example to Tennenbaum’s Theorem. In this paper we extend the q-naturals to the Q-Universe and explore the properties of the various subsets along the way. In the process of this development, we realize that the standard Universe and the Q-Universe are simply the zeroth-order and first-order Universes, respectively, in a countable subsumption hierarchy of recursive Universes; there exist countably many counter-examples to Tennenbaum’s Theorem.

Comments: 100 Pages.

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Submission history

[v1] 2017-07-11 17:00:37
[v2] 2017-08-05 15:40:50

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